A four-point nonlocal integral boundary value problem for fractional differential equations of arbitrary order

• Main Authors: Bashir Ahmad, Sotiris Ntouyas
• Format: Article
• Language: English
• Published: University of Szeged 2011-04-01
• Series: Electronic Journal of Qualitative Theory of Differential Equations
• Subjects: fractional differential equations; four-point integral boundary conditions; existence; fixed point theorem; leray-schauder degree
• Online Access: http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1&paramtipus_ertek=publication&param_ertek=585
• ISSN: 1417-3875; 1417-3875

This paper studies a nonlinear fractional differential equation of an arbitrary order with four-point nonlocal integral boundary conditions. Some existence results are obtained by applying standard fixed point theorems and Leray-Schauder degree theory. The involvement of nonlocal parameters in four-point integral boundary conditions of the problem makes the present work distinguished from the available literature on four-point integral boundary value problems which mainly deals with the four-point boundary conditions restrictions on the solution or gradient of the solution of the problem. These integral conditions may be regarded as strip conditions involving segments of arbitrary length of the given interval. Some illustrative examples are presented.