A new computational for approximate analytical solutions of nonlinear time-fractional wave-like equations with variable coefficients

Ali Khalouta; Abdelouahab Kadem; Ali Khalouta; Abdelouahab Kadem

doi:10.3934/math.2020001

AIMS Mathematics

2020, Volume 5, Issue 1: 1-14. doi: 10.3934/math.2020001

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A new computational for approximate analytical solutions of nonlinear time-fractional wave-like equations with variable coefficients

Ali Khalouta ^,,
Abdelouahab Kadem

Laboratory of Fundamental and Numerical Mathematics, Department of Mathematics, Faculty of Sciences, Ferhat Abbas University of Sétif 1, Sétif 19000, Algeria

Received: 08 July 2019 Accepted: 25 September 2019 Published: 15 October 2019
MSC : Primary: 35R11, 26A33; Secondary: 74G10, 35C05

The main purpose of this paper is to present a new computational for approximate analytical solutions of nonlinear time-fractional wave-like equations with variable coefficients using the fractional residual power series method (FRPSM). The fractional derivative is considered in the Caputo sense. This method is based on the generalized Taylor series formula and residual error function. Unlike other analytical methods, FRPSM has a special advantage, that it solves the nonlinear problems without using linearization, discretization, perturbation or any other restrictions. By numerical examples, it is shown that the FRPSM is a simple, effective, and powerful method for finding approximate analytical solutions of nonlinear fractional partial differential equations.
- nonlinear time-fractional wave-like equations,
- Caputo fractional derivative,
- fractional residual power series method
Citation: Ali Khalouta, Abdelouahab Kadem. A new computational for approximate analytical solutions of nonlinear time-fractional wave-like equations with variable coefficients[J]. AIMS Mathematics, 2020, 5(1): 1-14. doi: 10.3934/math.2020001

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Abstract

The main purpose of this paper is to present a new computational for approximate analytical solutions of nonlinear time-fractional wave-like equations with variable coefficients using the fractional residual power series method (FRPSM). The fractional derivative is considered in the Caputo sense. This method is based on the generalized Taylor series formula and residual error function. Unlike other analytical methods, FRPSM has a special advantage, that it solves the nonlinear problems without using linearization, discretization, perturbation or any other restrictions. By numerical examples, it is shown that the FRPSM is a simple, effective, and powerful method for finding approximate analytical solutions of nonlinear fractional partial differential equations.

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