Utilization of the Modified Adomian Decomposition Method on the Bagley-Torvik Equation Amidst Dirichlet Boundary Conditions

Authors

DOI:

https://doi.org/10.29020/nybg.ejpam.v17i1.5050

Keywords:

Fractional calculus; Bagley-Torvik equation; Dirichlet boundary condition; Modified Adomian decomposition method; Boundary-value probleFractional Calculus; Modified Adomian decomposition method; Boundary value problem.

Abstract

The Bagley-Torvik equation is an imperative differential equation that considerably arises in various branches of mathematical physics and mechanics. However, very few methods exist for the treatment of the model analytically; in fact, researchers frequently shop for semi-analytical and numerical methods in their studies. Therefore, the main goal of this research is to find the
exact analytical solution for the fractional Bagley-Torvik equation fitted with Dirichlet boundary data, as well as a system of fractional Bagley-Torvik equations. Thus, this research aims to show that the modified Adomian decomposition method (MADM) via the proposed two algorithms is a very effective method for treating a class of Bagley-Torvik equations endowed with Dirichlet
boundary data. Certainly, MADM is a very powerful approach for solving dissimilar functional equations without the need for either linearization, discretization, perturbation, or even unnecessary restraining postulations. Additionally, the method reveals exact analytical solutions whenever obtainable or closed-form series solutions whenever exact solutions are not feasible. Lastly, some illustrative test problems of the governing model are examined to demonstrate the superiority of the proposed algorithms.

Author Biographies

  • Mariam Al-Mazmumy
  • Mona Alsulami

    Department of Mathematics and Statistics, Faculty of Science, University of Jeddah

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Published

2024-01-31

Issue

Section

Nonlinear Analysis

How to Cite

Utilization of the Modified Adomian Decomposition Method on the Bagley-Torvik Equation Amidst Dirichlet Boundary Conditions. (2024). European Journal of Pure and Applied Mathematics, 17(1), 546-568. https://doi.org/10.29020/nybg.ejpam.v17i1.5050