Existence Results on Nonlinear Fractional Differential Inclusions

In this paper, we study the existence of solution for a boundary value problem of nonlinear fractional di fferential inclusion of order alpha is an element of (0, 1) with initial boundary value problems (BVP for short) and the standard Riemann-Liouville fractional derivative. Our approach is based on the topological transversality method in fixed point theory. we use a powerful method due to Granas to prove the existence of solution to BVP. Granas method is commonly as topological transversality and relies on the idea of an essential map. The method has been highly useful proving existence of solutions for initial and boundary value problem for integer order differential equations.