Affiliation:
1. Faculty of Architecture and Engineering Rauf Denktaş University Nicosia Northern Cyprus Turkey
2. Department of Mathematics, Faculty of Arts and Sciences Eastern Mediterranean University Famagusta Northern Cyprus Turkey
Abstract
Linear fractional differential equations with variable coefficients and various types of fractional derivatives can be solved explicitly, using either fixed‐point theorems and successive approximations or Green's functions. In this paper, we consider a multi‐term fractional differential equation with continuous variable coefficients and incommensurate fractional orders, and we construct an explicit solution by a direct method of successive approximations, which is made rigorous by checking the solution function explicitly via substitution. The results are obtained for the most general initial value problem of an inhomogeneous equation with inhomogeneous initial conditions, the first time that an explicit analytical solution has been found for this general problem. Special cases are provided to illustrate the main results, and connections are discussed with previous results in the literature.
Subject
General Engineering,General Mathematics