Application of MHPM for Solving Semi-Linear Fractional Differential Equations

Abstract

In this paper, we have introduced a general class of semi-linear first-order fractional differential equations (FrDEs) which is modified mathematically in many problems in many significant fields of applied science and engineering. The homotopy perturbation method (HPM) has been modified for solving generalized linear first-order FrDEs. Also, we have tested the modified homotopy perturbation method (MHPM) on the solving of different implementations of problems which show the accuracy and efficiency of the proposed method. The approximated solutions of the tested problems using MHPM are agree well with analytical solutions. However, these solutions proved that the proposed method to be high accurate and efficient method. MHPM has been used for solving class of generalized factional Riccati DE. The approximated solution of a class of nonlinear Riccati FrDE has been studied. Also, we have tested the MHPM on the solving of different implementations of this class which are show the accuracy and efficiency of the proposed method. The approximated solutions using proposed MHPM of the tested problems are agree well with analytical solutions and they proved to be more accurate.