Tbilisi Mathematical Journal

An efficient method for solving nonlinear time-fractional wave-like equations with variable coefficients

Ali Khalouta and Abdelouahab Kadem

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Abstract

In this paper, fractional residual power series method (FRPSM) is effectively applied for finding the approximate analytical solutions of general nonlinear time-fractional wave-like equations with variable coefficients. This method based on constructing series solutions in a form of rapidly convergent series with easily computable components and without need of linearization, discretization, perturbation or unrealistic assumptions. Numerical results are given and then they are compared with the exact solutions both numerically and graphically. By numerical examples, it is shown that the FRPSM is very simple, efficient and convenient for solving different forms of nonlinear fractional partial differential equations.

Note

The authors would like to thank Professor Hvedri Inassaridze (Editor-in-Chief) as well as the anonymous referees who has made valuable and careful comments, which improved the paper considerably.

Article information

Source
Tbilisi Math. J., Volume 12, Issue 4 (2019), 131-147.

Dates
Received: 10 May 2019
Accepted: 30 October 2019
First available in Project Euclid: 3 January 2020

Permanent link to this document
https://projecteuclid.org/euclid.tbilisi/1578020573

Digital Object Identifier
doi:10.32513/tbilisi/1578020573

Mathematical Reviews number (MathSciNet)
MR4047581

Zentralblatt MATH identifier
07104577

Subjects
Primary: 35R11: Fractional partial differential equations
Secondary: 26A33: Fractional derivatives and integrals 35C05: Solutions in closed form 74G10: Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.)

Keywords
general nonlinear time-fractional wave-like equations approximate analytical solutions Caputo fractional derivative fractional residual power series method

Citation

Khalouta, Ali; Kadem, Abdelouahab. An efficient method for solving nonlinear time-fractional wave-like equations with variable coefficients. Tbilisi Math. J. 12 (2019), no. 4, 131--147. doi:10.32513/tbilisi/1578020573. https://projecteuclid.org/euclid.tbilisi/1578020573


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