Homotopy Analysis Integral Transform Method for the Solutions of Fractional Order Integro-differential Equations

Document Type : Regular research papers

Authors

1 Department of Mathematics, Faculty of Physical Sciences, University of Ilorin, Ilorin, Nigeria.

2 Department of Mathematics, Faculty of Physical Sciences, University of Ilorin, Nigeria.

3 Directorate of General Studies (Mathematics Unit), Federal School of Surveying, Oyo, Nigeria.

Abstract

The main thrust of this research is to propose a reliable method for the solution of a class of fractional order integro-differential equations with difference kernel. The integro-differential equations considered are both linear and nonlinear type with the fractional order derivative interpreted in Caputo sense. The proposed method combined Shehu transform with the Homotopy Analysis Method. The essence of the HAM is to overcome any nonlinearity that may be encountered in the problem with the aid of Homotopy derivative, while Shehu transform is chosen as result of the unique advantage that it handles bothe constant and variable coefficients problems, unlike the Laplace transform. The Homotopy Analysis Integral Transform Method (HAITM) developed is applied to some problems in the literature and the results are either the exact solution (when such exits) or at the minimum in truncated series which in all cases agree with those in the literature. The results are presented in tabular form, as well as in 2D graphs. The computations are implemented in Mathematica 13.3.

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