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Multi-term fractional boundary value problems with four-point boundary conditions

In this paper, we study a new class of boundary value problems for Caputo-type multi-term fractional differential equations and inclusions with four-point boundary conditions. In case of the single-valued problem, we apply Sadovski fixed point theorem, Banach contraction mapping principle and Leray-Schauder nonlinear alternative to derive the existence results, while the multi-valued problem is studied with the aid of nonlinear alternative for contractive maps and Covitz-Nadler fixed point theorem. We illustrate the obtained results with examples. Boundary value problems involving Riemann-Liouville type multi-term fractional differential equations and inclusions are also described.