Dr. Muhammad Usman

Contact me

  •   Department of Mathematics
  •   (051)-9265100
  •   dr.usman@numl.edu.pk

Dr. Muhammad Usman

Assistant Professor

PhD Mathematics: Peking University, Beijing, China

Distinguished Scholar

September 2015 - January 2019

Specialized in applied Mathematics including numerical solutions of partial differential equations, mathematical modelling, fractional calculus, solitary wave theory, analytical and semi-analytical techniques, spectral methods and fluid mechanics.

Thesis title: Numerical and Wavelets Algorithms for Problems Arising in Engineering and Mathematical Physics

MS Mathematics: HITEC University, Taxila, Pakistan

Gold Medalist

September 2011 - July 2013

Studies focused on semi analytical schemes, wavelets based methods, soliton wave solutions and fractional calculus.

Thesis title: Some Efficient Algorithms for Differential Equations

BS Mathematics: GC University, Faisalabad, Pakistan

Gold Medalist

September 2007 - July 2011

Specialized in both pure and applied mathematics.

Assistant Professor: National University of Modern Languages (NUML), Islamabad, Pakistan

September 2021-to date

I am working here assistant professor and teaching various course and undergraduate and post-graduate level for engineering and mathematics students. I am also supervising graduate students.

Assistant Professor: Riphah International University, Faisalabad Campus, Pakistan

March 2021-August 2021

I was working there as visiting assistant professor and taught Advanced Numerical Analysis course to M. Phil mathematics students.

Postdoctoral Researcher: Peking University, Beijing, China

April 2019-March 2021

I have completed postdoc under BOYA postdoc fellowship under the advisor Prof. Moubin Liu. I worked on heat transfer analysis of cavity problems and modified/extended algorithms to investigate the numerical solutions of fractional-order problems.

Lecturer: University of Wah, Wah, Pakistan

September 2013-July 2015

I have taught the metric spaces, classical mechanics, partial differential equations, vector calculus and complex variables and transform to the students of BS and MSc mathematics, electrical engineering and mechatronics engineering.

Teaching Assistant: HITEC University, Taxila, Pakistan

September 2012-July 2014

During this job I assist dean faculty of sciences in preparing the lectures of differential equations, partial differential equations, boundary values problems, integral equations and perturbation methods, assignments/quizzes marking and making results.

Lecturer: Government Degree College, Taxila, Pakistan

September 2014-August 2015

I also performed duty as CTI where I taught mathematics at intermediate level.

  1. T. Zubair, M. Usman, U. Nazir, P. Kumam, M. Sohail, Numerical Exploration via Least Squares Estimation on Three Dimensional MHD Yield Exhibiting Nanofluid Model with Porous Stretching Boundaries, Fractal and Fractional, 5 (2021): 167. October 14, 2021. [Link]
  2. M. N. Nguyen, T. Sajjad, T. H. Le, R. U. Haq, M. Usman, A. Koonsrisook, Modified Chebyshev wavelets approach for mixed convection flow due to oblique stagnation point along a vertically moving surface with zero mass flux of nanoparticles, Journal of Molecular Liquid, 343 (2021): 117569. December 1, 2021. [Link]
  3. T. Zubair, M. Usman*, M. Hamid, M. Sohail, U. Nazir, K. S. Nisar, V. Vijayakumar, Computational analysis of radiative Williamson hybrid nanofluid comprising variable thermal conductivity, Japanese Journal of Applied Physics, 60(8) (2021): 087004. August 2, 2021. [Link]
  4. M. Hamid, M. Usman*, R. U. Haq, W. Wang, An efficient spectral based analysis to nonlinear oscillatory problems, Chaos, Soliton and Fractals. 146 (2021): 110921. May 1, 2021. [Link]
  5. T. Zubair, T. Lu, M. Usman*, Higher dimensional semi-relativistic time-fractional Vlasov-Maxwell code for numerical simulation based on linear polarization and 2D Landau damping instability, Applied Mathematics and Computation, 401 (2021): 126100. July 15, 2021. [Link]
  6. M. Usman*, M. Hamid, Z. H. Khan, R. U. Haq, Neuronal Dynamics and Electrophysiology Fractional Model: A Modified Wavelet Approach, Physica A: Statistical Mechanics and its Applications, 570 (2021): 125805. March 15, 2021. [Link]
  7. T. Zubair, T. Lu, S. K. Nisar, M. Usman*, A semi-relativistic time-fractional Vlasov-Maxwell code for numerical simulation based on circular polarization and symmetric two-stream instability, Results in Physics, 22 (2021): 103932. March 1, 2021. [Link]
  8. M. Usman*, M. Hamid, M. B. Liu, Novel operational matrices-based hybrid computational scheme for a class of fractional-order Burger equations in multidimensions, Chaos Soliton and Fractals, 144 (2021): 110701. March 1, 2021. [Link]
  9. M. Usman*, M. Hamid, R. U. Haq, M. B. Liu, Linearized novel operational matrices-based scheme for classes of nonlinear time-space fractional unsteady problems in 2D, Applied Numerical Mathematics, 162 (2021): 351-373. April 1, 2021. [Link]
  10. M. Hamid, M. Usman*, W. Wang, Z. F. Tian, A Galerkin Approach to Analyze MHD Flow of Nanofluid along Converging/Diverging Channels, Archive of Applied Mechanics. (2020): 1-8. January 24, 2021. [Link]
  11. M. Usman*, M. Hamid, M. B. Liu, Higher-order algorithms for stable solutions of unsteady time-fractional nonlinear Telegraph equations in space, Numerical Methods for Partial Differential Equations, doi.org/10.1002/num.22744. January 20, 2021. [Link]

[2020]

  1. M. Usman*, T. Zubair, M. Hamid, R. U. Haq, Z. H. Khan, Unsteady Flow and Heat Transfer of Tangent Hyperbolic Fluid: Legendre Wavelets Based Analysis, Heat Transfer, 50(4): 3079-3093. December 7, 2020. [Link]
  2. T. Zubair, M. Usman*, A semi-reativistic time-fractional Vlasov-Maxwell code for numerical simulation based on circular polarization and Landau damping instability, Numerical Methods for Partial Differential Equations. (Accepted)
  3. M. Hamid, M. Usman*, R. U. Haq, Z. F. Tian, W. Wang, Linearized stable spectral method to analyze two-dimensional nonlinear evolutionary and reaction-diffusion models, Numerical Methods for Partial Differential Equations, 2020;1-19. November 17, 2020. [Link]
  4. Z. H. Khan, M. Usman, T. Zubair, M. Hamid, R. U. Haq, Brownian motion and thermophoresis effects on unsteady stagnation point flow of Eyring-Powell nanofluid: A Galerkin approach, Communications in Theoretical Physics, 72(12), p.125005. November 24, 2020. [Link]
  5. M. Hamid, M. Usman*, W. Wang, F. Z. Tian, A stable computational approach to analyze semi-relativistic behavior of fractional evolutionary problems, Numerical Methods for Partial Differential Equations, 2020;1-15. doi.org/10.1002/num.22617. November 3, 2020. [Link]
  6. T. Zubair, L. Tiao, M. Usman*, A novel scheme for time-fractional semi-reativistic Vlasov-Maxwell system based on Laser-Plasma interaction with linear polarization and Landau damping instability, Numerical Methods for Partial Differential Equations, 2020. doi.org/10.1002/num.22611. November 16, 2020. [Link]
  7. M. Hamid, M. Usman*, W. Wang, Z. F. Tian, Hybrid Fully Spectral Linearized Scheme for Time-Fractional Evolutionary Equations, Mathematical Methods in the Applied Sciences, 2020;1-23. [Link]
  8. M. Usman, M. Hamid, Z. H. Khan, R. U. Haq, W. Ahmed, Finite element analysis of water-based ferrofluid flow in a partially heated triangular cavity, International Journal of Numerical Methods for Heat and Fluid Flow. November 23, 2020. [Link]
  9. M. Hamid, O. M. Foong, M. Usman, I. Khan, W. Wang, A new operational matrices based spectral method for multi-order fractional problems, Symmetry, 12(9) (2020): 1471. September 1, 2020. [Link]
  10. M. Usman*, M. Hamid, M, S. Khalid, R. U. Haq, M. B. Liu, A robust scheme based on novel-operational matrices for some classes of time-fractional nonlinear problems arising in mechanics and mathematical physics, Numerical Methods for Partial Differential Equations, 36(6) (2020): 1566-1600. November 1, 2020. [Link]
  11. M. Usman*, M. Hamid, T. Zubair, R. U. Haq, W. Wang, M. B. Liu, Novel operational matrices-based method for solving fractional-order Delay differential equations via shifted Gegenbauer polynomials, Applied Mathematics and Computation, 372 (2020): 124985. May 1, 2020. [Link]
  12. M. Usman*, T. Zubair, M. Hamid, R. U. Haq, Novel modification in Wavelets Method to Analyze Unsteady Flow of Nanofluid Between two Infinitely Parallel Plates, Chinese Journal of Physics, 66 (2020): 222-236. May 6, 2020. [Link]
  13. M. Hamid, M. Usman*, R.U. Haq, W. Wang, A Chelyshkov polynomial based algorithm to analyze the transport dynamics and anomalous diffusion in fractional model, Physica A: Statistical Mechanics and its Applications, (2020): 124227. January 20, 2020. [Link]
  14. R. U. Haq, M. Usman, E. A. Algehyne, Natural convection of CuO-water nanofluid filled in a partially heated corrugated cavity: KKL model approach, Communications in Theoretical Physics, 72 (8) (2020): 085003. July 20, 2020. [Link]
  15. U. Ali, M. Sohail, M. Usman, F. A. Abdullah, I. Khan, K. S. Nisar, Fourth-order difference approximation for time-fractional modified sub-diffusion equation, Symmetry, 12 (5) (2020): 691. May 1, 2020. [Link]
  16. T. K. Nguyen, M. Usman, M. Sheikholeslami, R. U. Haq, A. Shafee, A. K. Jilani, I. Tlili, Numerical analysis of MHD flow and nanoparticle migration within a permeable space containing Non-equilibrium model, Physica A: Statistical Mechanics and its Applications, 537 (2020): 122459. January 1, 2020. [Link]
  17. Z. H. Khan, W. A. Khan, R. U. Haq, M. Usman, M. Hamid, Effects of volume fraction on water-based carbon nanotubes flow in a right-angle trapezoidal cavity: FEM based analysis, International Communications in Heat and Mass Transfer, 116 (2020): 104640. July 1, 2020. [Link]

[2019]

  1. M. Usman, Z. H. Khan, M. B. Liu, MHD natural convection and thermal control inside a cavity with obstacles under the radiation effects, Physica A: Statistical Mechanics and its Applications, 535 (2019), 122443. December 1, 2019. [Link]
  2. M. Usman, M. Hamid, T. Zubair, R. U. Haq, W. Wang, Operational matrix-based algorithm for partial differential equations of fractional-order with Dirichlet boundary conditions, The European Physical Journal Plus, 134(6) (2019): 279. June 1, 2019. [Link]
  3. M. Hamid, M. Usman, Z. H. Khan, R. U. Haq, W. Wang, Heat transfer and flow analysis of Casson fluid in a partially heated trapezoidal cavity, International Communications in Heat and Mass Transfer, 108 (2019): 104284. November 1, 2019. [Link]
  4. M. Hamid, M. Usman, Z. H. Khan, W. Wang, R. Ahmad, Dual solutions and stability analysis of flow and heat transfer of Casson fluid on a stretching sheet with convective boundary condition, Physics Letters A, 383 (2019): 2400-2408. July 18, 2019. [Link]
  5. M. Hamid, M. Usman, T. Zubair, R. U. Haq, A. Shafee, An efficient analysis for N-soliton, Lump and Lump-kink solutions of time-fractional (2+1)-Kadomtsev-Petviashvili equation, Physica A: Statistical Mechanics and its Applications, 528 (2019) 121320. August 15, 2019. [Link]
  6. M. Hamid, M. Usman*, T. Zubair, R, U. Haq, W. Wang, Innovative operational matrices based computational scheme for fractional diffusion problems with the Riesz derivative, The European Physical Journal Plus, 134(10) (2019): 484. October 1, 2019. [Link]
  7. M. Hamid, M. Usman*, R. U. Haq, Wavelets investigation of Soret and Dufour effects on stagnation point fluid flow in two-dimension with variable thermal conductivity and diffusivity, Physica Scripta, 94 (2019): 115219. August 21, 2019. [Link]
  8. M. Hamid, M. Usman, R. U. Haq, Z. H. Khan, W. Wang, Wavelets analysis of stagnation point flow of non-Newtonian Nanofluid, Applied Mathematics and Mechanics (English Edition), 40(8) (2019): 1211-1226. August 1, 2019. [Link]
  9. T. A. Alkanhal, M. Sheikholeslami, M. Usman, R. U. Haq, A. Shafee, A. S. Al-Ahmadi, I. Tlili, Thermal management of MHD nanofluid within the porous medium enclosed in a wavy shaped cavity with square obstacle in the presence of radiation heat source, International Journal of Heat and Mass Transfer, 139 (2019), 87-94. August 1, 2019. [Link]
  10. M. Hamid, T. Zubair, M. Usman, Z. H. Khan, W. Wang, Natural convection effects on heat and mass transfer of slip flow of time-dependent Prandtl fluid, Journal of Computational Design and Engineering, 6(4) (2019): 584-592. October 1, 2019. [Link]
  11. M. Hamid, T. Zubair, M. Usman*, R. U. Haq, Numerical investigation of fractional-order unsteady natural convective radiating flow of nanofluid in a vertical channel, AIMS Mathematics, 4(5) (2019): 1416-1429. August 14, 2019. [Link]
  12. M. Usman, M. Hamid, M. M. Rashidi, Gegenbauer wavelets collocation-based scheme to explore the solution of free bio-convection of nanofluid in 3D nearby stagnation point, Neural Computing & Applications, 31(11) (2019): 8003-8019. November 1, 2019. [Link]

 

[2018]

  1. M. Hamid, M. Usman, T. Zubair, R. U. Haq, W. Wang, Shape effects of MoS2 nanoparticles on rotating flow of nanofluid in three-dimension over a stretching surface with dependent thermal conductivity, International Journal of Heat and Mass Transfer, 124 (2018): 706-714. September 1, 2018. [Link]
  2. M. Usman, F. A. Soomro, R. U. Haq, W. Wang, Thermal and velocity slip effects on Casson Nanofluid flow over an inclined permeable stretching cylinder via collocation method, International Journal of Heat and Mass Transfer, 122 (2018): 1255-1263. July 1, 2018. [Link]
  3. M. Usman, M. Hamid, T. Zubair, R. U. Haq, W. Wang, Cu-Al2O3/Water hybrid nanofluid through a permeable surface presence of nonlinear radiation and variable thermal conductivity via LSM approach, International Journal of Heat and Mass Transfer, 126 (2018): 1347-1356. November 1, 2018. [Link]
  4. M. Usman, M. Hamid, R. U. Haq, W. Wang, Heat and fluid flow of water and ethylene-glycol based Cu-nanoparticles between two parallel squeezing porous disks: LSGM approach, International Journal of Heat and Mass Transfer, 123 (2018): 888-895. August 1, 2018. [Link]
  5. M. Usman*, M. Hamid, U. Khan, S. T. Mohyud-Din, M. A. Iqbal, W. Wang, Differential transform method for unsteady nanofluid flow and heat transfer, Alexandria Engineering Journal, 57 (2018):1867-1875. September 1, 2018. [Link]
  6. M. Usman, M. Hamid, S. T. Mohyud-Din, A. Waheed, W. Wang, Exploration of uniform heat flux on the flow and heat transportation of Ferrofluids along a smooth plate: Comparative investigation, International Journal of Biomathematics, 11(2) (2018): 1850048. May 4, 2018. [Link]
  7. M. Usman, M. Hamid, R. U. Haq, W. Wang, An efficient algorithm based on Gegenbauer wavelets for the solutions of variable-order fractional differential equations, The European Physical Journal Plus, 133 (2018): 327. August 1, 2018. [Link]
  8. M. Usman, R. U. Haq, M. Hamid, W. Wang, Least square study of heat transfer of water based Cu and Ag nanoparticles along a converging/diverging channel, Journal of Molecular Liquid, 249 (2018): 856-867. January 1, 2018. [Link]
  9. M. Usman, T. Zubair, M. Hamid, R. U. Haq, W. Wang, Wavelets solution of MHD 3-D fluid flow in the presence of slip and thermal radiation effects, Physics of Fluids, 30(2) (2018): 023104. February 15, 2018. [Link]
  10. M. Hamid, M. Usman, T. Zubair, S. T. Mohyud-Din, Comparison of Lagrange multipliers for telegraph equations, Ain Shams Engineering Journal, 9(4) (2018): 2323-2328. December 1, 2018. [Link]
  11. M. Hamid, M. Usman, Z. H. Khan, R. U. Haq, W. Wang, Numerical study of unsteady MHD flow of Williamson Nanofluid in a permeable channel with heat source/sink and thermal radiation, The European Physical Journal Plus, 133 (2018): 527. December 1, 2018. [Link]
  12. S. T. Mohyud Din, M. Usman, W. Wang, M. Hamid, A study of heat transfer analysis for squeezing flow of a Casson fluid via differential transform method, Neural Computing & Applications, 30(10) (2018): 3253-3264. November 1, 2018. [Link]
  13. F. A. Soomro, M. Usman, R. U. Haq, W. Wang, Melting heat transfer analysis of Sisko fluid over a moving surface with nonlinear thermal radiation via Collocation Method, International Journal of Heat and Mass Transfer, 126 (2018): 1034-1042. November 1, 2018. [Link]
  14. F. A. Soomro, M. Usman, R. U. Haq, Thermal and velocity slip effects on MHD mixed convection flow of Williamson Nanofluid along a vertical surface: Modified Legendre wavelets approach, Physica E: Low-dimensional System and Nanostructure, 104 (2018): 130-137. October 1, 2018. [Link]
  15. S. T. Mohyud-Din, T. Zubair, M. Usman, M. Hamid, M. Rafiq, S. Mohsin, Investigation of heat and mass transfer under the influence of variable diffusion coefficient and thermal conductivity, Indian Journal of Physics, 92(9) (2018): 1109-1117. September 1, 2018. [Link]

 

[2017]

  1. S. T. Mohyud-Din, M. Usman, K. Afaq, M. Hamid, W. Wang, Examination of carbon-water Nanofluid flow with thermal radiation under the effect of Marangoni convection, Engineering Computations, 34(7) (2017): 2330-2343. October 2, 2017. [Link]
  2. S. T. Mohyud-Din, M. Usman, B. Bin-Mohsin, A study of heat and mass transfer of Nanofluids arising in Biosciences using Buongiorno's model, International Journal of Computational Methods, 14(02) (2017), 1750018. March 7, 2017. [Link]

Fractional calculus

Spectral methods

Fluid mechanics

Mathematical modelling

Numerical solution of PDEs

Analytical and semi-analytical techniques

Solitary wave solutions

Education

PhD Mathematics: Peking University, Beijing, China

Distinguished Scholar

September 2015 - January 2019

Specialized in applied Mathematics including numerical solutions of partial differential equations, mathematical modelling, fractional calculus, solitary wave theory, analytical and semi-analytical techniques, spectral methods and fluid mechanics.

Thesis title: Numerical and Wavelets Algorithms for Problems Arising in Engineering and Mathematical Physics

MS Mathematics: HITEC University, Taxila, Pakistan

Gold Medalist

September 2011 - July 2013

Studies focused on semi analytical schemes, wavelets based methods, soliton wave solutions and fractional calculus.

Thesis title: Some Efficient Algorithms for Differential Equations

BS Mathematics: GC University, Faisalabad, Pakistan

Gold Medalist

September 2007 - July 2011

Specialized in both pure and applied mathematics.

Experience

Assistant Professor: National University of Modern Languages (NUML), Islamabad, Pakistan

September 2021-to date

I am working here assistant professor and teaching various course and undergraduate and post-graduate level for engineering and mathematics students. I am also supervising graduate students.

Assistant Professor: Riphah International University, Faisalabad Campus, Pakistan

March 2021-August 2021

I was working there as visiting assistant professor and taught Advanced Numerical Analysis course to M. Phil mathematics students.

Postdoctoral Researcher: Peking University, Beijing, China

April 2019-March 2021

I have completed postdoc under BOYA postdoc fellowship under the advisor Prof. Moubin Liu. I worked on heat transfer analysis of cavity problems and modified/extended algorithms to investigate the numerical solutions of fractional-order problems.

Lecturer: University of Wah, Wah, Pakistan

September 2013-July 2015

I have taught the metric spaces, classical mechanics, partial differential equations, vector calculus and complex variables and transform to the students of BS and MSc mathematics, electrical engineering and mechatronics engineering.

Teaching Assistant: HITEC University, Taxila, Pakistan

September 2012-July 2014

During this job I assist dean faculty of sciences in preparing the lectures of differential equations, partial differential equations, boundary values problems, integral equations and perturbation methods, assignments/quizzes marking and making results.

Lecturer: Government Degree College, Taxila, Pakistan

September 2014-August 2015

I also performed duty as CTI where I taught mathematics at intermediate level.

Publications

  1. T. Zubair, M. Usman, U. Nazir, P. Kumam, M. Sohail, Numerical Exploration via Least Squares Estimation on Three Dimensional MHD Yield Exhibiting Nanofluid Model with Porous Stretching Boundaries, Fractal and Fractional, 5 (2021): 167. October 14, 2021. [Link]
  2. M. N. Nguyen, T. Sajjad, T. H. Le, R. U. Haq, M. Usman, A. Koonsrisook, Modified Chebyshev wavelets approach for mixed convection flow due to oblique stagnation point along a vertically moving surface with zero mass flux of nanoparticles, Journal of Molecular Liquid, 343 (2021): 117569. December 1, 2021. [Link]
  3. T. Zubair, M. Usman*, M. Hamid, M. Sohail, U. Nazir, K. S. Nisar, V. Vijayakumar, Computational analysis of radiative Williamson hybrid nanofluid comprising variable thermal conductivity, Japanese Journal of Applied Physics, 60(8) (2021): 087004. August 2, 2021. [Link]
  4. M. Hamid, M. Usman*, R. U. Haq, W. Wang, An efficient spectral based analysis to nonlinear oscillatory problems, Chaos, Soliton and Fractals. 146 (2021): 110921. May 1, 2021. [Link]
  5. T. Zubair, T. Lu, M. Usman*, Higher dimensional semi-relativistic time-fractional Vlasov-Maxwell code for numerical simulation based on linear polarization and 2D Landau damping instability, Applied Mathematics and Computation, 401 (2021): 126100. July 15, 2021. [Link]
  6. M. Usman*, M. Hamid, Z. H. Khan, R. U. Haq, Neuronal Dynamics and Electrophysiology Fractional Model: A Modified Wavelet Approach, Physica A: Statistical Mechanics and its Applications, 570 (2021): 125805. March 15, 2021. [Link]
  7. T. Zubair, T. Lu, S. K. Nisar, M. Usman*, A semi-relativistic time-fractional Vlasov-Maxwell code for numerical simulation based on circular polarization and symmetric two-stream instability, Results in Physics, 22 (2021): 103932. March 1, 2021. [Link]
  8. M. Usman*, M. Hamid, M. B. Liu, Novel operational matrices-based hybrid computational scheme for a class of fractional-order Burger equations in multidimensions, Chaos Soliton and Fractals, 144 (2021): 110701. March 1, 2021. [Link]
  9. M. Usman*, M. Hamid, R. U. Haq, M. B. Liu, Linearized novel operational matrices-based scheme for classes of nonlinear time-space fractional unsteady problems in 2D, Applied Numerical Mathematics, 162 (2021): 351-373. April 1, 2021. [Link]
  10. M. Hamid, M. Usman*, W. Wang, Z. F. Tian, A Galerkin Approach to Analyze MHD Flow of Nanofluid along Converging/Diverging Channels, Archive of Applied Mechanics. (2020): 1-8. January 24, 2021. [Link]
  11. M. Usman*, M. Hamid, M. B. Liu, Higher-order algorithms for stable solutions of unsteady time-fractional nonlinear Telegraph equations in space, Numerical Methods for Partial Differential Equations, doi.org/10.1002/num.22744. January 20, 2021. [Link]

[2020]

  1. M. Usman*, T. Zubair, M. Hamid, R. U. Haq, Z. H. Khan, Unsteady Flow and Heat Transfer of Tangent Hyperbolic Fluid: Legendre Wavelets Based Analysis, Heat Transfer, 50(4): 3079-3093. December 7, 2020. [Link]
  2. T. Zubair, M. Usman*, A semi-reativistic time-fractional Vlasov-Maxwell code for numerical simulation based on circular polarization and Landau damping instability, Numerical Methods for Partial Differential Equations. (Accepted)
  3. M. Hamid, M. Usman*, R. U. Haq, Z. F. Tian, W. Wang, Linearized stable spectral method to analyze two-dimensional nonlinear evolutionary and reaction-diffusion models, Numerical Methods for Partial Differential Equations, 2020;1-19. November 17, 2020. [Link]
  4. Z. H. Khan, M. Usman, T. Zubair, M. Hamid, R. U. Haq, Brownian motion and thermophoresis effects on unsteady stagnation point flow of Eyring-Powell nanofluid: A Galerkin approach, Communications in Theoretical Physics, 72(12), p.125005. November 24, 2020. [Link]
  5. M. Hamid, M. Usman*, W. Wang, F. Z. Tian, A stable computational approach to analyze semi-relativistic behavior of fractional evolutionary problems, Numerical Methods for Partial Differential Equations, 2020;1-15. doi.org/10.1002/num.22617. November 3, 2020. [Link]
  6. T. Zubair, L. Tiao, M. Usman*, A novel scheme for time-fractional semi-reativistic Vlasov-Maxwell system based on Laser-Plasma interaction with linear polarization and Landau damping instability, Numerical Methods for Partial Differential Equations, 2020. doi.org/10.1002/num.22611. November 16, 2020. [Link]
  7. M. Hamid, M. Usman*, W. Wang, Z. F. Tian, Hybrid Fully Spectral Linearized Scheme for Time-Fractional Evolutionary Equations, Mathematical Methods in the Applied Sciences, 2020;1-23. [Link]
  8. M. Usman, M. Hamid, Z. H. Khan, R. U. Haq, W. Ahmed, Finite element analysis of water-based ferrofluid flow in a partially heated triangular cavity, International Journal of Numerical Methods for Heat and Fluid Flow. November 23, 2020. [Link]
  9. M. Hamid, O. M. Foong, M. Usman, I. Khan, W. Wang, A new operational matrices based spectral method for multi-order fractional problems, Symmetry, 12(9) (2020): 1471. September 1, 2020. [Link]
  10. M. Usman*, M. Hamid, M, S. Khalid, R. U. Haq, M. B. Liu, A robust scheme based on novel-operational matrices for some classes of time-fractional nonlinear problems arising in mechanics and mathematical physics, Numerical Methods for Partial Differential Equations, 36(6) (2020): 1566-1600. November 1, 2020. [Link]
  11. M. Usman*, M. Hamid, T. Zubair, R. U. Haq, W. Wang, M. B. Liu, Novel operational matrices-based method for solving fractional-order Delay differential equations via shifted Gegenbauer polynomials, Applied Mathematics and Computation, 372 (2020): 124985. May 1, 2020. [Link]
  12. M. Usman*, T. Zubair, M. Hamid, R. U. Haq, Novel modification in Wavelets Method to Analyze Unsteady Flow of Nanofluid Between two Infinitely Parallel Plates, Chinese Journal of Physics, 66 (2020): 222-236. May 6, 2020. [Link]
  13. M. Hamid, M. Usman*, R.U. Haq, W. Wang, A Chelyshkov polynomial based algorithm to analyze the transport dynamics and anomalous diffusion in fractional model, Physica A: Statistical Mechanics and its Applications, (2020): 124227. January 20, 2020. [Link]
  14. R. U. Haq, M. Usman, E. A. Algehyne, Natural convection of CuO-water nanofluid filled in a partially heated corrugated cavity: KKL model approach, Communications in Theoretical Physics, 72 (8) (2020): 085003. July 20, 2020. [Link]
  15. U. Ali, M. Sohail, M. Usman, F. A. Abdullah, I. Khan, K. S. Nisar, Fourth-order difference approximation for time-fractional modified sub-diffusion equation, Symmetry, 12 (5) (2020): 691. May 1, 2020. [Link]
  16. T. K. Nguyen, M. Usman, M. Sheikholeslami, R. U. Haq, A. Shafee, A. K. Jilani, I. Tlili, Numerical analysis of MHD flow and nanoparticle migration within a permeable space containing Non-equilibrium model, Physica A: Statistical Mechanics and its Applications, 537 (2020): 122459. January 1, 2020. [Link]
  17. Z. H. Khan, W. A. Khan, R. U. Haq, M. Usman, M. Hamid, Effects of volume fraction on water-based carbon nanotubes flow in a right-angle trapezoidal cavity: FEM based analysis, International Communications in Heat and Mass Transfer, 116 (2020): 104640. July 1, 2020. [Link]

[2019]

  1. M. Usman, Z. H. Khan, M. B. Liu, MHD natural convection and thermal control inside a cavity with obstacles under the radiation effects, Physica A: Statistical Mechanics and its Applications, 535 (2019), 122443. December 1, 2019. [Link]
  2. M. Usman, M. Hamid, T. Zubair, R. U. Haq, W. Wang, Operational matrix-based algorithm for partial differential equations of fractional-order with Dirichlet boundary conditions, The European Physical Journal Plus, 134(6) (2019): 279. June 1, 2019. [Link]
  3. M. Hamid, M. Usman, Z. H. Khan, R. U. Haq, W. Wang, Heat transfer and flow analysis of Casson fluid in a partially heated trapezoidal cavity, International Communications in Heat and Mass Transfer, 108 (2019): 104284. November 1, 2019. [Link]
  4. M. Hamid, M. Usman, Z. H. Khan, W. Wang, R. Ahmad, Dual solutions and stability analysis of flow and heat transfer of Casson fluid on a stretching sheet with convective boundary condition, Physics Letters A, 383 (2019): 2400-2408. July 18, 2019. [Link]
  5. M. Hamid, M. Usman, T. Zubair, R. U. Haq, A. Shafee, An efficient analysis for N-soliton, Lump and Lump-kink solutions of time-fractional (2+1)-Kadomtsev-Petviashvili equation, Physica A: Statistical Mechanics and its Applications, 528 (2019) 121320. August 15, 2019. [Link]
  6. M. Hamid, M. Usman*, T. Zubair, R, U. Haq, W. Wang, Innovative operational matrices based computational scheme for fractional diffusion problems with the Riesz derivative, The European Physical Journal Plus, 134(10) (2019): 484. October 1, 2019. [Link]
  7. M. Hamid, M. Usman*, R. U. Haq, Wavelets investigation of Soret and Dufour effects on stagnation point fluid flow in two-dimension with variable thermal conductivity and diffusivity, Physica Scripta, 94 (2019): 115219. August 21, 2019. [Link]
  8. M. Hamid, M. Usman, R. U. Haq, Z. H. Khan, W. Wang, Wavelets analysis of stagnation point flow of non-Newtonian Nanofluid, Applied Mathematics and Mechanics (English Edition), 40(8) (2019): 1211-1226. August 1, 2019. [Link]
  9. T. A. Alkanhal, M. Sheikholeslami, M. Usman, R. U. Haq, A. Shafee, A. S. Al-Ahmadi, I. Tlili, Thermal management of MHD nanofluid within the porous medium enclosed in a wavy shaped cavity with square obstacle in the presence of radiation heat source, International Journal of Heat and Mass Transfer, 139 (2019), 87-94. August 1, 2019. [Link]
  10. M. Hamid, T. Zubair, M. Usman, Z. H. Khan, W. Wang, Natural convection effects on heat and mass transfer of slip flow of time-dependent Prandtl fluid, Journal of Computational Design and Engineering, 6(4) (2019): 584-592. October 1, 2019. [Link]
  11. M. Hamid, T. Zubair, M. Usman*, R. U. Haq, Numerical investigation of fractional-order unsteady natural convective radiating flow of nanofluid in a vertical channel, AIMS Mathematics, 4(5) (2019): 1416-1429. August 14, 2019. [Link]
  12. M. Usman, M. Hamid, M. M. Rashidi, Gegenbauer wavelets collocation-based scheme to explore the solution of free bio-convection of nanofluid in 3D nearby stagnation point, Neural Computing & Applications, 31(11) (2019): 8003-8019. November 1, 2019. [Link]

 

[2018]

  1. M. Hamid, M. Usman, T. Zubair, R. U. Haq, W. Wang, Shape effects of MoS2 nanoparticles on rotating flow of nanofluid in three-dimension over a stretching surface with dependent thermal conductivity, International Journal of Heat and Mass Transfer, 124 (2018): 706-714. September 1, 2018. [Link]
  2. M. Usman, F. A. Soomro, R. U. Haq, W. Wang, Thermal and velocity slip effects on Casson Nanofluid flow over an inclined permeable stretching cylinder via collocation method, International Journal of Heat and Mass Transfer, 122 (2018): 1255-1263. July 1, 2018. [Link]
  3. M. Usman, M. Hamid, T. Zubair, R. U. Haq, W. Wang, Cu-Al2O3/Water hybrid nanofluid through a permeable surface presence of nonlinear radiation and variable thermal conductivity via LSM approach, International Journal of Heat and Mass Transfer, 126 (2018): 1347-1356. November 1, 2018. [Link]
  4. M. Usman, M. Hamid, R. U. Haq, W. Wang, Heat and fluid flow of water and ethylene-glycol based Cu-nanoparticles between two parallel squeezing porous disks: LSGM approach, International Journal of Heat and Mass Transfer, 123 (2018): 888-895. August 1, 2018. [Link]
  5. M. Usman*, M. Hamid, U. Khan, S. T. Mohyud-Din, M. A. Iqbal, W. Wang, Differential transform method for unsteady nanofluid flow and heat transfer, Alexandria Engineering Journal, 57 (2018):1867-1875. September 1, 2018. [Link]
  6. M. Usman, M. Hamid, S. T. Mohyud-Din, A. Waheed, W. Wang, Exploration of uniform heat flux on the flow and heat transportation of Ferrofluids along a smooth plate: Comparative investigation, International Journal of Biomathematics, 11(2) (2018): 1850048. May 4, 2018. [Link]
  7. M. Usman, M. Hamid, R. U. Haq, W. Wang, An efficient algorithm based on Gegenbauer wavelets for the solutions of variable-order fractional differential equations, The European Physical Journal Plus, 133 (2018): 327. August 1, 2018. [Link]
  8. M. Usman, R. U. Haq, M. Hamid, W. Wang, Least square study of heat transfer of water based Cu and Ag nanoparticles along a converging/diverging channel, Journal of Molecular Liquid, 249 (2018): 856-867. January 1, 2018. [Link]
  9. M. Usman, T. Zubair, M. Hamid, R. U. Haq, W. Wang, Wavelets solution of MHD 3-D fluid flow in the presence of slip and thermal radiation effects, Physics of Fluids, 30(2) (2018): 023104. February 15, 2018. [Link]
  10. M. Hamid, M. Usman, T. Zubair, S. T. Mohyud-Din, Comparison of Lagrange multipliers for telegraph equations, Ain Shams Engineering Journal, 9(4) (2018): 2323-2328. December 1, 2018. [Link]
  11. M. Hamid, M. Usman, Z. H. Khan, R. U. Haq, W. Wang, Numerical study of unsteady MHD flow of Williamson Nanofluid in a permeable channel with heat source/sink and thermal radiation, The European Physical Journal Plus, 133 (2018): 527. December 1, 2018. [Link]
  12. S. T. Mohyud Din, M. Usman, W. Wang, M. Hamid, A study of heat transfer analysis for squeezing flow of a Casson fluid via differential transform method, Neural Computing & Applications, 30(10) (2018): 3253-3264. November 1, 2018. [Link]
  13. F. A. Soomro, M. Usman, R. U. Haq, W. Wang, Melting heat transfer analysis of Sisko fluid over a moving surface with nonlinear thermal radiation via Collocation Method, International Journal of Heat and Mass Transfer, 126 (2018): 1034-1042. November 1, 2018. [Link]
  14. F. A. Soomro, M. Usman, R. U. Haq, Thermal and velocity slip effects on MHD mixed convection flow of Williamson Nanofluid along a vertical surface: Modified Legendre wavelets approach, Physica E: Low-dimensional System and Nanostructure, 104 (2018): 130-137. October 1, 2018. [Link]
  15. S. T. Mohyud-Din, T. Zubair, M. Usman, M. Hamid, M. Rafiq, S. Mohsin, Investigation of heat and mass transfer under the influence of variable diffusion coefficient and thermal conductivity, Indian Journal of Physics, 92(9) (2018): 1109-1117. September 1, 2018. [Link]

 

[2017]

  1. S. T. Mohyud-Din, M. Usman, K. Afaq, M. Hamid, W. Wang, Examination of carbon-water Nanofluid flow with thermal radiation under the effect of Marangoni convection, Engineering Computations, 34(7) (2017): 2330-2343. October 2, 2017. [Link]
  2. S. T. Mohyud-Din, M. Usman, B. Bin-Mohsin, A study of heat and mass transfer of Nanofluids arising in Biosciences using Buongiorno's model, International Journal of Computational Methods, 14(02) (2017), 1750018. March 7, 2017. [Link]

Interests

Fractional calculus

Spectral methods

Fluid mechanics

Mathematical modelling

Numerical solution of PDEs

Analytical and semi-analytical techniques

Solitary wave solutions