MULTI-TERM FRACTIONAL DIFFERENTIAL EQUATIONS AND INCLUSIONS WITH GENERALIZED NONLOCAL FRACTIONAL INTEGRO-DIFFERENTIAL BOUNDARY CONDITIONS

In this paper, we study a new class of boundary value problems involving multiple fractional derivatives of Caputo type and generalized nonlocal fractional integro-differential boundary conditions. For the single-valued case, two existence results are obtained by means of nonlinear alternative of the Leray-Schauder type and the Krasnoselski's fixed point theorem, while the uniqueness of solutions is established by applying the contraction mapping principle. For the multi-valued case, two existence results are obtained by means of the Krasnoselski's multi-valued fixed point theorem and nonlinear alternative for contractive mappings. Examples illustrating the main results are also presented.