Semi-analytical and numerical computation of fractal-fractional sine-Gordon equation with non-singular kernels-Reference-Cited by-同舟云学术

Semi-analytical and numerical computation of fractal-fractional sine-Gordon equation with non-singular kernels

Published:2022 Issue:8 Volume:7 Page:14975-14990
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Ali Amir¹,Khan Abid Ullah¹,Algahtani Obaid²,Saifullah Sayed¹

Affiliation:

1. Department of Mathematics, University of Malakand, Chakdara, Dir(L), Khyber Pakhtunkhwa, Pakistan

2. Department of Mathematics, College of Sciences, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

Abstract

<abstract><p>In this article, we study the nonlinear sine-Gordon equation (sGE) under Mittag-Leffler and exponential decay type kernels in a fractal fractional sense. The Laplace Adomian decomposition method (LADM) is applied to investigate the sGE under the above-mentioned operators. The convergence analysis is provided for the proposed method. The results are validated by considering numerical examples with different initial conditions for both kernels and confirm the competence of the proposed technique. It is revealed that the obtained series solutions of the model with fractal fractional operators converge to the exact solutions. The numerical results converge to the particular exact solutions, proving the significance of LADM for nonlinear systems under fractal fractional derivatives. The absolute error analysis between the exact and obtained series solutions with both operators is shown in the tabulated form. The physical interpretations of the attained results with different fractal and fractional parameters are discussed in detail.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

Reference37 articles.

1. K. B. Oldham, J. Spanier, The fractional calculus, New York: Academic Press, 1974.

2. K. S. Miller, B. Ross, An introduction to the fractional calculus and fractional differential equations, New York: John Wiley and Sons Inc, 1993.

3. I. Podlubny, Fractional differential equations, San Diego: Academic Press, 1999.

4. R. Hilfer, Foundations of fractional dynamics, Fractals, 3 (1995), 549–556.

5. R. Hilfer, Fractional diffusion based on Riemman–Liouville fractional derivatives, J. Phys. Chem. B, 104 (2000), 3914–3917. https://doi.org/10.1021/jp9936289

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