Analytic Solution of Linear Fractional Differential Equations with Constant Coefficient

Abstract

This paper presents direct methods for obtaining the explicit general solution to a linear sequential fractional differential equation (LSFDE), involving Jumarie’s modification of Riemann–Liouville derivative, with constant coefficients. The general solution to a homogenous LSFDE with constant coefficients is obtained by using the roots of the characteristic polynomial of the corresponding homogeneous equation. For the non-homogeneous case, two methods, undetermined coefficients and variation of parameter, are investigated to find the particular solution. The method of undetermined coefficients is independent of the integral transforms while the method of variation of parameter is not. Moreover, several examples are illustrative for demonstrating the advantage of our approach.

Keywords: Fractional differential equations, Riemann–Liouville derivative, Caputo derivative, undetermined coefficients, variation of parameter.