On System of Time-Fractional Partial Differential Equations

Authors

  • Umer HAYAT Department of Mathematics, HITEC University, Taxila Cantt
  • Abid KAMRAN Department of Mathematics, HITEC University, Taxila Cantt
  • Ambreen BIBI Department of Mathematics, HITEC University, Taxila Cantt
  • Ahmet YILDIRIM Zeytinalani Mah, Urla-Izmir
  • Syed Tauseef MOHYUD-DIN Department of Mathematics, HITEC University, Taxila Cantt

Keywords:

Fractional partial differential equations, homotopy perturbation method, Laplace transform, system of PDEs, HPTM

Abstract

In this paper, we apply Homotopy Perturbation Transformation Method (HPM) using the Laplace transformation to tackle time-fractional systems of Partial Differential equations. The proposed technique is fully compatible with the complexity of these problems and obtained results are highly encouraging. Numerical results coupled with graphical representations explicitly reveal the complete reliability and efficiency of the suggested algorithm.

Downloads

Download data is not yet available.

Metrics

Metrics Loading ...

Author Biography

Syed Tauseef MOHYUD-DIN, Department of Mathematics, HITEC University, Taxila Cantt

Department of Mathematics, HITEC University

References

S Abbasbandy. Numerical method for non-linear wave and diffusion equations equation by the variational iteration method. Int. J. Numer. Meth. Eng. 2008; 73, 1836-43.

S Abbasbandy. Numerical solutions of nonlinear Klein-Gordon equation by variational iteration method. Int. J. Numer. Meth. Eng. 2007; 70, 876-81.

MA Abdou and AA Soliman. New applications of variational iteration method. Phys. D 2005; 211, 1-8.

A Ghorbani and JS Nadjfi. He’s homotopy perturbation method for calculating Adomian’s polynomials. Int. J. Nonlinear Sci. Numer. Simulat. 2007; 8, 229-332.

JH He. Some asymptotic methods for strongly nonlinear equation. Int. J. Mod. Phys. 2006; 20, 1144-99.

JH He. Some applications of nonlinear fractional differential equations and their approximations. Bull. Sci. Technol. 1999; 15, 86-90.

WX Ma and RG Zhou. Nonlinearization of spectral problems for the perturbation KdV systems. Phys. A 2001; 296, 60-74.

WX Ma and M Chen. Hamiltonian and quasi-Hamiltonian structures associated with semi-direct sums of Lie algebras. J. Phys. A Math. Gen. 2006; 39, 10787-801.

S Momani. An algorithm for solving the fractional convection-diffusion equation with nonlinear source term. Comm. Nonlinear Sci. Numer. Simulat. 2007; 12, 1283-90.

ST Mohyud-Din, MA Noor and KI Noor. Some relatively new techniques for nonlinear problems. Math. Probl. Eng. 2009; 2009, 234849.

ST Mohyud-Din and MA Noor. Homotopy perturbation method for solving fourth-order boundary value problems. Math. Prob. Eng. 2007; 2007, 98602.

ST Mohyud-Din and MA Noor. Homotopy perturbation method for solving partial differential equations. Zeitschrift für Naturforschung A 2008; 64a, 1-14.

ST Mohyud-Din. Variational Iteration Techniques for Boundary Value Problems. VDM Verlag, German, 2010, p. 1.196.

ST Mohyud-Din, MA Noor, KI Noor and MM Hosseini. Solution of singular equations by He’s variational iteration method. Int. J. Nonlinear Sci. Numer. Simulat. 2010; 11, 81-6.

ST Mohyud-Din, MA Noor and KI Noor. Travelling wave solutions of seventh-order generalized KdV equations using He’s polynomials. Int. J. Nonlinear Sci. Numer. Simulat. 2009; 10, 223-9.

Z Odibat and S Momani. Numerical solution of Fokker-Planck equation with space-and time-fractional derivatives. Phys. Lett. A 2007; 369, 349-58.

I Podlubny. Fractional differential equations. New York, Academic Press, 1999.

A Yıldırım and H Koçak. Homotopy perturbation method for solving the space-time fractional advection-dispersion equation. Adv. Water Resour. 2009; 32, 1711-6.

A Yildirim and ST Mohyud-Din. Analytical approach to space and time fractional Burger’s equations. Chin. Phys. Lett. 2010; 27, 090501.

AM Wazwaz. The modified decomposition method and Pade approximants for solving Thomas-Fermi equation. Appl. Math. Comput. 1999; 105, 11-9.

L Xu. He’s homotopy perturbation method for a boundary layer equation in unbounded domain. Comput. Math. Appl. 2007; 54, 1067-70.

WX Ma. Linear superposition principle applying to Hirota bilinear equations. Comput. Math. Appl. 2011; 61, 950-9.

WX Ma, Y Zhang, Y Tang and J Tu. Hirota bilinear equations with linear subspaces of solutions. Appl. Math. Comput. 2012; 218, 7174-83.

WX Ma, B Fuchssteiner. Explicit and exact solutions to a Kolmogorov-Petrovskii-Piskunov equation. Int. J. Nonlin. Mech. 1996; 31, 329-38.

WX Ma. A Transformed rational function method and exact solution to the 3+1 dimension Jimbo-Miwa equation. Chaos Soliton. Fract. 2009; 42, 1356-63.

Downloads

Published

2013-07-01

How to Cite

HAYAT, U., KAMRAN, A., BIBI, A., YILDIRIM, A., & MOHYUD-DIN, S. T. (2013). On System of Time-Fractional Partial Differential Equations. Walailak Journal of Science and Technology (WJST), 10(5), 437–448. Retrieved from https://wjst.wu.ac.th/index.php/wjst/article/view/317

Most read articles by the same author(s)