On the numerical solution of fractional order differential equations using transforms and quadrature

Abstract

In this work, we extended the work of [12] to approximate the solution of fractional order differential equations by an integral representation in the complex plane. The resultant integral is approximated to high order accuracy using quadrature. The accuracy of the method depends on the selection of optimal contour of integration. Several contour have been proposed in the literature for solving fractional differential equations. In the present work, we will investigate the applicability of the recently developed optimal contour in [16] for solving fractional differential equations. Various fractional order differential equations are approximated and the results are compared with other methods to demonstrate the efficiency and accuracy of the method for various optimal contour of integrations.