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The existence and uniqueness of solutions for a class of nonlinear fractional differential equations with infinite delay. (English) Zbl 1277.34110

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.

MSC:

34K37 Functional-differential equations with fractional derivatives
47N20 Applications of operator theory to differential and integral equations
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