Solutions of Fractional Differential Equations using Fractional Laplace Transform & Shehu Transform Method

Abstract

In the present paper, we discussed the application of Shehu transform as well as α-Integral Laplace transform to solve homogenous and non-homogenous linear fractional differential equations using Riemann-Liouville differential operator. α-Integral Laplace transform is a generalization of the Laplace transform both classical sense of the definition as in their properties and theorems. In this work we study the response of the α-Integral Laplace transform introduced in [6] on the fractional derivative of Riemann-Liouville. Shehu transform is a generalization of the Laplace and the Sumudu integral transform for solving fractional differential equations in the time domain and is applied to both ordinary and fractional differential equations to show its simplicity, efficiency and the high accuracy. Some examples are included to show the validity and applicability of the presented methods. Solving some problems show that the Shehu and Fractional Laplace transforms are powerful and efficient techniques for obtaining analytic solution of homogenous and non-homogenous linear fractional differential equations and are in uniformity with the solutions available in the literature.