The Numerical Solutions of Nonlinear Time-Fractional Differential Equations by LMADM

Hameeda Oda  AL-Humedi; Faeza Lafta  Hasan

doi:10.24996/ijs.2021.SI.2.2

Authors

Hameeda Oda AL-Humedi Department of Mathematics, College of Education for Pure Sciences, Basrah University, Basrah, Iraq
Faeza Lafta Hasan Department of Mathematics, College of Education for Pure Sciences, Basrah University, Basrah, Iraq

DOI:

https://doi.org/10.24996/ijs.2021.SI.2.2

Keywords:

Fractional order differential equations, Caputo fractional derivative, Laplace Transform, Adomian decomposition methods

Abstract

This paper presents a numerical scheme for solving nonlinear time-fractional differential equations in the sense of Caputo. This method relies on the Laplace transform together with the modified Adomian method (LMADM), compared with the Laplace transform combined with the standard Adomian Method (LADM). Furthermore, for the comparison purpose, we applied LMADM and LADM for solving nonlinear time-fractional differential equations to identify the differences and similarities. Finally, we provided two examples regarding the nonlinear time-fractional differential equations, which showed that the convergence of the current scheme results in high accuracy and small frequency to solve this type of equations.