The existence and uniqueness of solutions for a class of nonlinear fractional differential equations with infinite delay (Q370056)

Summary: 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 \(\Omega = \{y : (-\infty, b] \to \mathbb R : y \mid_{(-\infty, 0]} \in \mathcal B\}\) such that \(y \mid_{[0, b]}\) is continuous and \(\mathcal B\) is a phase space.