Work

Stability Analysis Study of Time-Fractional Nonlinear Modified Kawahara Equation Based on the Homotopy Perturbation Sadik Transform

Year: 2024

Type: article

Abstract: In this manuscript, we survey a numerical algorithm based on the combination of the homotopy perturbation method and the Sadik transform for solving the time-fractional nonlinear modified shallow water waves (called Kawahara equation) within the frame of the Caputo–Prabhakar (CP) operator. The nonlinear terms are handled with the assistance of the homotopy polynomials. The stability analysis of the implemented method is studied by using S-stable mapping and the Banach contraction principle. Also, we use the fixed-point method to determine the existence and uniqueness of solutions in the given suggested model. Finally, some numerical simulations are illustrated to display the accuracy and efficiency of the present numerical method. Moreover, numerical behaviors are captured to validate the reliability and efficiency of the scheme.

Source: Fractal and Fractional

DOI: 10.3390/fractalfract8090512

Authors: Zhihua Chen, Saeed Kosari, Jana Shafi, Mohammad Hossein Derakhshan

Institutions: Guangzhou University, Prince Sattam Bin Abdulaziz University

Language: English

Topic: Fractional Differential Equations Solutions

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,069

Funder: National Natural Science Foundation of China