Existence of positive solutions for boundary value problems of fractional functional differential equations

Chuanzhi Bai, Huaiyin Normal University, Huaian, Jiangsu, P. R. China

E. J. Qualitative Theory of Diff. Equ., No. 30. (2010), pp. 1-14.

Abstract: This paper deals with the existence of positive solutions for a boundary value problem involving a nonlinear functional differential equation of fractional order $\alpha$ given by $ D^{\alpha} u(t) + f(t, u_t) = 0$, $t \in (0, 1)$, $2 < \alpha \le 3$, $ u^{\prime}(0) = 0$, $u^{\prime}(1) = b u^{\prime}(\eta)$, $u_0 = \phi$. Our results are based on the nonlinear alternative of Leray-Schauder type and Krasnosel'skii fixed point theorem.

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