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Existence Results for Nonlinear Fractional Differential Equations with Four-Point Nonlocal Type Integral Boundary Conditions

Volume 11, Number 1 (2011), 29 - 39

Existence Results for Nonlinear Fractional Differential Equations with Four-Point Nonlocal Type Integral Boundary Conditions

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Abstract

In this paper, we investigate some new existence results for nonlinear fractional differential equations of order $q \in (1,2]$ with four-point nonlocal integral boundary conditions by applying standard fixed point theorems and Leray-Schauder degree theory. Our results are new in the sense that the nonlocal parameters in four-point integral boundary conditions for the problem appear in the integral part of the conditions in contrast to the available literature on four-point fractional boundary value problems which deals with the four-point boundary conditions restrictions on the solution or gradient of the solution of the problem. Some illustrative examples are presented.