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Zbl 1204.34005
Ahmad, Bashir; Ntouyas, Sotiris K.; Alsaedi, Ahmed
New existence results for nonlinear fractional differential equations with three-point integral boundary conditions. (English)
[J] Adv. Difference Equ. 2011, Article ID 107384, 11 p. (2011). ISSN 1687-1847/e

Summary: This paper studies a boundary value problem of nonlinear fractional differential equations of order $q \in (1,2]$ with three-point integral boundary conditions. Some new existence and uniqueness results are obtained by using standard fixed point theorems and Leray-Schauder degree theory. Our results are new in the sense that the nonlocal parameter in three-point integral boundary conditions appears in the integral part of the conditions in contrast to the available literature on three-point boundary value problems which deals with the three-point boundary conditions restrictions on the solution or gradient of the solution of the problem. Some illustrative examples are also discussed.

MSC 2000:: *34A08

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