The Existence and Uniqueness of Solutions for a Class of Nonlinear Fractional Differential Equations with Infinite Delay

We prove the existence and uniqueness of solutions for two classes of infinite delay nonlinear fractional order differential equations involving Riemann-Liouville fractional derivatives. The analysis is based on the alternative of the Leray-Schauder fixed-point theorem, the Banach fixed-point theorem, and the Arzela-Ascoli theorem in Ω={y:(−∞,b]→ℝ:y|(−∞,0]∈ℬ} such that y|[0,b] is continuous and ℬ is a phase space