Fractional-order multivalued problems with non-separated integral-flux boundary conditions

Abstract

In this paper, we study the existence of solutions for a new kind of boundary value problem of Caputo type fractional differential inclusions with non-separated local and nonlocal integral-flux boundary conditions. We apply appropriate fixed point theorems for multivalued maps to obtain the existence results for the given problems covering convex as well as non-convex cases for multivalued maps. We also include Riemann-Stieltjes integral conditions in our discussion. Some illustrative examples are also presented. The paper concludes with some interesting observations.

Keywords

• fractional differential inclusions; integral; flux; boundary conditions; fixed point