Some boundary value problems of fractional differential equations and inclusions

Authors:
Bashir Ahmad;Juan J. Nieto;Johnatan Pimentel
Affiliations:
Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia;Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Santiago de Compostela, 15782, Santiago de Compostela, Spain;Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Santiago de Compostela, 15782, Santiago de Compostela, Spain
Venue:
Computers & Mathematics with Applications
Year:
2011

Citing 3
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Abstract

In this paper, we study the existence of solutions for nonlinear fractional differential equations and inclusions of order q@?(1,2] with families of mixed and closed boundary conditions. In case of inclusion problems, the existence results are established for convex as well as nonconvex multivalued maps. Our results are based on Leray-Schauder degree theory, nonlinear alternative of Leray-Schauder type, and some fixed point theorems for multivalued maps. Some interesting special cases are also discussed.