We established the existence of a positive solution of nonlinear fractional differential equations , with finite delay , , where , that is, is singular at and $. The operator of involves the Riemann-Liouville fractional derivatives. In this problem, the initial conditions with fractional order and some relations among them were considered. The analysis rely on the alternative of the Leray-Schauder fixed point theorem, the Banach fixed point theorem, and the Arzela-Ascoli theorem in a cone.
Azizollah Babakhani. Dumitru Baleanu. "Existence of Positive Solutions for a Class of Delay Fractional Differential Equations with Generalization to N-Term." Abstr. Appl. Anal. 2011 1 - 14, 2011. https://doi.org/10.1155/2011/391971