Fractional differential equations with continuous variable coefficients and Sonine kernels

Abstract

We study linear fractional ODEs with continuous variable coefficients and general fractional derivative (GFD) operators of Riemann-Liouville and Caputo types defined using Sonine kernels. Using the Banach fixed point theorem, we prove existence and uniqueness of solution functions in suitable function spaces, and we construct these solutions explicitly by means of locally uniformly convergent infinite series involving Sonine kernels. This work is done both for the classical Luchko-type GFDs with Sonine kernels, and for the m-fold versions of these operators.