An application of fixed point theory in fractional differential inclusions

This article studies the existence of solutions for a fractional differential inclusion D^α u(t)+D^β u(t)ϵ F(t,u(t)) ,tϵ J=[0,1] u(0)=0 where 0 β α 1 and D^α, D^β is the standard Riemann-Liouville fractional derivative, F:J×R^n→P(R^n) is a Caratheodory multifunction, Here P(R^n ) denotes the family of all nonempty subsets of R^n. Our approach is based on the topological transversality method in fixed point theory. Keywords: Riemann-Liouville derivative, Fixed point, Fractional differential.