New Existence Results for Nonlinear Fractional Differential Equations with Three-Point Integral Boundary Conditions

By Bashir Ahmad, Sotiris K. Ntouyas, Ahmed Alsaedi. 2011

194 citations recorded by the source corpus.

This paper studies a boundary value problem of nonlinear fractional differential equations of order 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.

Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/136fa5443d6169d7c6501b59ca4ba9c08d84d2a5

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In Applied Mathematics

In Modeling and Simulation

In Numerical Analysis

Citations in the corpus

On Hadamard fractional integro-differential boundary value problems (2015, background): “For the recent development of the topic, we refer the reader to a series of books and papers [1–13].”
A fully Hadamard type integral boundary value problem of a coupled system of fractional differential equations (2014, background): “For some recent development on the topic, see [1], [2], [4], [5], [6], [7], [8], [9], [10], [11], [12], [14], [17], and the references therein.”