Abstract
In this paper, we establish sufficient conditions for the existence and uniqueness of solutions for boundary value problems of Hadamard-type fractional functional differential equations and inclusions involving both retarded and advanced arguments. We make use of the standard tools of fixed point theory to obtain the main results.
Highlights
Differential equations of fractional order play a very important role in describing many real world phenomena
Functional differential equations arise in a variety of areas of biological, physical, and engineering applications, see, for example, the books of Kolmanovskii and Myshkis [ ] and Hale and Verduyn Lunel [ ], and the references cited therein
In this paper, motivated by [ ], we study boundary value problems of Hadamard-type fractional functional differential equations and inclusions involving both retarded and advanced arguments
Summary
Differential equations of fractional order play a very important role in describing many real world phenomena. In Section , we present the existence results for convex and nonconvex multi-valued maps involved in the problem ( )-( ) which, respectively, rely on the nonlinear alternative of Leray-Schauder type and a fixed point theorem for contractive multi-valued maps due to Covitz and Nadler. A multi-valued map G : J → Pcl(X) is said to be measurable if, for each x ∈ E, the function Y : J → X defined by
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