Soliton Solution of the Nonlinear Time Fractional Equations: Comprehensive Methods to Solve Physical Models-Reference-Cited by-同舟云学术

Soliton Solution of the Nonlinear Time Fractional Equations: Comprehensive Methods to Solve Physical Models

Published:2024-01-30 Issue:2 Volume:13 Page:92
ISSN:2075-1680
Container-title:Axioms
language:en
Short-container-title:Axioms

Author:

O’Regan Donal¹^ORCID,Aderyani Safoura Rezaei²^ORCID,Saadati Reza²^ORCID,Inc Mustafa³⁴^ORCID

Affiliation:

1. School of Mathematical and Statistical Sciences, University of Galway, University Road, H91 TK33 Galway, Ireland

2. School of Mathematics, Iran University of Science and Technology, Narmak, Tehran 13114-16846, Iran

3. Department of Mathematics, Science Faculty, Firat University, Elazig 23119, Turkey

4. Department of Medical Research, China Medical University, Taichung 40402, Taiwan

Abstract

In this paper, we apply two different methods, namely, the G′G-expansion method and the G′G2-expansion method to investigate the nonlinear time fractional Harry Dym equation in the Caputo sense and the symmetric regularized long wave equation in the conformable sense. The mentioned nonlinear partial differential equations (NPDEs) arise in diverse physical applications such as ion sound waves in plasma and waves on shallow water surfaces. There exist multiple wave solutions to many NPDEs and researchers are interested in analytical approaches to obtain these multiple wave solutions. The multi-exp-function method (MEFM) formulates a solution algorithm for calculating multiple wave solutions to NPDEs and at the end of paper, we apply the MEFM for calculating multiple wave solutions to the (2 + 1)-dimensional equation.

Publisher

MDPI AG

Subject

Geometry and Topology,Logic,Mathematical Physics,Algebra and Number Theory,Analysis

Link

https://www.mdpi.com/2075-1680/13/2/92/pdf

Reference37 articles.

1. The exact solutions of the conformable time-fractional modified nonlinear Schrödinger equation by the Trial equation method and modified Trial equation method;Aderyani;Adv. Math. Phys.,2022

2. The exact solutions of conformable time-fractional modified nonlinear Schrödinger equation by first integral method and functional variable method;Aderyani;Opt. Quantum Electron.,2022

3. Aderyani, S.R., Saadati, R., O’Regan, D., and Alshammari, F.S. (2022). Describing Water Wave Propagation Using the G′G–Expansion Method. Mathematics, 11.

4. New optical solitons based on the perturbed Chen-Lee-Liu model through Jacobi elliptic function method;Tarla;Opt. Quantum Electron.,2022

5. Yasmin, H., Aljahdaly, N.H., Saeed, A.M., and Shah, R. (2023). Probing families of optical soliton solutions in fractional perturbed Radhakrishnan–Kundu–Lakshmanan model with improved versions of extended direct algebraic method. Fractal Fract., 7.