Boundary value problem of fractional differential inclusions involving Caputo-Fabrizio time-fractional derivative without singular kernel

A new definition of fractional derivative has recently been put forward, which solves many challenging problems in the field of fractional calculus. This derivative has no singular kernel named Caputo-Fabrizio time-fractional derivative (t-FD). Under this new definition, we investigate a class of boundary value problem (BVP) of fractional differential inclusions (FDI). By means of endpoint theory and Leary-Schauder alternative, the existence of solutions are generated. This is the first work dealing with BVP of FDI involving Caputo-Fabrizio (t-FD). Effectiveness of the obtained theoretical results is illustrated by several examples.