Approximate Solution of Nonlinear Time-Fractional PDEs by Laplace Residual Power Series Method

Hussam Aljarrah, Mohammad Alaroud, Anuar Ishak and Maslina Darus
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Hussam Aljarrah: Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia (UKM), Bangi 43600, Selangor, Malaysia
Mohammad Alaroud: Department of Mathematics, Faculty of Arts and Science, Amman Arab University, Amman 11953, Jordan
Anuar Ishak: Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia (UKM), Bangi 43600, Selangor, Malaysia
Maslina Darus: Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia (UKM), Bangi 43600, Selangor, Malaysia

Mathematics, 2022, vol. 10, issue 12, 1-16

Abstract: Most physical phenomena are formulated in the form of non-linear fractional partial differential equations to better understand the complexity of these phenomena. This article introduces a recent attractive analytic-numeric approach to investigate the approximate solutions for nonlinear time fractional partial differential equations by means of coupling the Laplace transform operator and the fractional Taylor’s formula. The validity and the applicability of the used method are illustrated via solving nonlinear time-fractional Kolmogorov and Rosenau–Hyman models with appropriate initial data. The approximate series solutions for both models are produced in a rapid convergence McLaurin series based upon the limit of the concept with fewer computations and more accuracy. Graphs in two and three dimensions are drawn to detect the effect of time-Caputo fractional derivatives on the behavior of the obtained results to the aforementioned models. Comparative results point out a more accurate approximation of the proposed method compared with existing methods such as the variational iteration method and the homotopy perturbation method. The obtained outcomes revealed that the proposed approach is a simple, applicable, and convenient scheme for solving and understanding a variety of non-linear physical models.

Keywords: Riemann–Liouville fractional integral operator; fractional partial differential equations; Laplace power series method; inverse Laplace transform; time-Caputo fractional derivative (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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