Analytical Solution of Ordinary Fractional Differential Equations by Modified Homotopy Perturbation Method and Laplace Transform

Abstract

In this paper, a modified Laplace transform homotopy perturbation method (MLT-HPM) is used to find the approximate solution of ordinary fractional differential equations(OFDEs). The proposed method is developed to improve the accuracy of the approximate solutions provided by the LT-HPM method. The appropriate initial approximation will be chosen, furthermore, the residual error will be cancelled at several points of the interest interval (RECP). A couple of OFDEs are considered in order to demonstrate the effectiveness of the suggested method. Comparisons are made with the results obtained from LT-HPM, continuous analytical method (CAM), modified homotopy analysis method (MHAM), and modified optimal homotopy analysis method (MOHAM). The resulting solutions require only a first order approximation of MLT-HPM, compared to LT-HPM, which requires more iterations for the same examples studied.