On linear fractional differential equations with variable coefficients

Abstract

We study and solve linear ordinary differential equations , with fractional order derivatives of either Riemann-Liouville or Caputo types, and with variable coefficients which are ei-ther integrable or continuous functions. In each case, the solution is given explicitly by a convergent infinite series involving compositions of fractional integrals, and its uniqueness is proved in suitable function spaces using the Banach fixed point theorem. As a special case, we consider the case of constant coefficients, whose solutions can be expressed by using the multivariate Mittag-Leffler function. Some illustrative examples with potential applications are provided.(c) 2022 Elsevier Inc. All rights reserved.