Abstract
This study discussed the existence of solutions for a nonlinear fractional integro-differential equation of order with four-point nonlocal integral boundary conditions. The given problem is transformed to an equivalent fixed point problem in terms of an operator equation. Then, by means of Banach contraction principle and a fixed point theorem due to Krasnoselskii, the existence results are obtained. The last existence result is based on nonlinear alternative of Leray-Schauder type. An illustrative example is also presented. Key words: Integro-differential equations, fractional order, four-point integral boundary conditions, fixed point theorems, Leray-Schauder degree.
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