Existence results for nonlocal boundary value problems of fractional differential equations and inclusions with strip conditions
1 Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
2 Department of Mathematics, University of Ioannina 451 10 Ioannina, Greece
Boundary Value Problems 2012, 2012:55 doi:10.1186/1687-2770-2012-55Published: 9 May 2012
This article studies a new class of nonlocal boundary value problems of nonlinear differential equations and inclusions of fractional order with strip conditions. We extend the idea of four-point nonlocal boundary conditions to nonlocal strip conditions of the form: , . These strip conditions may be regarded as six-point boundary conditions. Some new existence and uniqueness results are obtained for this class of nonlocal problems by using standard fixed point theorems and Leray-Schauder degree theory. Some illustrative examples are also discussed.
MSC 2000: 26A33; 34A12; 34A40.