Solving fractional differential equations using fractional explicit method

Abstract

This research is focusing in solving the fractional differential equations (FDEs) for linear and non-linear type using fractional explicit method (FEM) with constant step-size. Most of the numerical methods for solving FDEs involved the interpolating points of step size ℎ. Some modifications were implemented in the derivation technique, where the step size 2ℎ are considered in the formula of the proposed method. The main goal of this research is to derive FEM by considering the implementation of second-order Adam-Bashforth method using Lagrange interpolation for fractional case. Besides, the order and convergence analysis of the developed method will also be investigated in this study. The algorithm of the proposed method is written in C language. Based on the numerical results obtained, it is clearly ratified that the proposed method converges as the step size, ℎ is getting smaller in solving the FDEs.