Weakly perturbed linear boundary-value problem for a system of multi-term fractional differential equations

Abstract

A weakly perturbed linear boundary-value problem for a system of multi-term fractional differential equations with Caputo derivatives is investigated. The case of commensurate orders of the derivatives is considered. We establish conditions under which the solution of the homogeneous generating boundary-value problem is not unique and the inhomogeneous generating boundary-value problem is unsolvable. We propose an iterative procedure for construction of a family of solutions of the posed problem.