Open AccessOn the Application of Homotopy Analysis Method to Fractional Differential Equations
Author(s) -
Khalid Suliman Aboodh,
Abu baker Ahmed
Publication year - 2021
Language(s) - English
Resource type - Journals
ISSN - 1858-6007
DOI - 10.52981/jfst.vi7.947
Subject(s) - homotopy analysis method , mathematics , convergence (economics) , fractional calculus , nonlinear system , homotopy perturbation method , exact solutions in general relativity , series (stratigraphy) , homotopy , matlab , differential equation , mathematical analysis , differential (mechanical device) , computer science , pure mathematics , paleontology , physics , quantum mechanics , economics , biology , economic growth , operating system , aerospace engineering , engineering
In this paper, an attempt has been made to obtain the solution of linear and nonlinear fractional differential equations by applying an analytic technique, namely the homotopy analysis method (HAM). The fractional derivatives are described by Caputo’s sense. By this method, the solution considered as the sum of an infinite series, which converges rapidly to exact solution with the help of the nonzero convergence control parameter ℏ. Some examples are given to show the efficiently and accurate of this method. The solutions obtained by this method has been compared with exact solution. Also our graphical represented of the solutions have been given by using MATLAB software.