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Zbl 1217.34007
Babakhani, Azizollah; Baleanu, Dumitru
Existence of positive solutions for a class of delay fractional differential equations with generalization to $N$-term. (English)
[J] Abstr. Appl. Anal. 2011, Article ID 391971, 14 p. (2011). ISSN 1085-3375; ISSN 1687-0409/e

Summary: We established the existence of a positive solution of nonlinear fractional differential equations $\frak L(D)[x(t) - x(0)] = f(t, x_t), t \in (0, b]$ with finite delay $x(t) = \omega(t), t \in [-\tau, 0]$, where $lim_{t \rightarrow 0} f(t, x_t) = +\infty$, that is, $f$ is singular at $t = 0$ and $x_t \in C([-\tau, 0], \Bbb R^{\geq 0}$. The operator of $\frak L(D)$ 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.

MSC 2000:: *34A08

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