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.
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