Abstract
We prove the existence of solutions for neutral functional differential inclusions involving Hadamard fractional derivatives by applying several fixed point theorems for multivalued maps. We also construct examples for illustrating the obtained results.
Highlights
Fractional calculus has emerged as an important area of investigation in view of the application of its tools in scientific and engineering disciplines
Our first existence result deals with the case when F has convex values and is based on nonlinear alternative for Kakutani maps [16] with the assumption that the multivalued map F is Carathéodory
In our first result (Theorem 1), we apply a nonlinear alternative for Kakutani multivalued maps to prove the existence of solutions for the problem at hand when the multivalued map F is assumed to be convex-valued
Summary
Fractional calculus has emerged as an important area of investigation in view of the application of its tools in scientific and engineering disciplines. An overwhelming interest in the subject of fractional-order differential equations and inclusions has been shown, for instance, see References [4,5,6,7,8,9,10,11,12,13,14] and the references cited therein. In Reference [15], the authors obtained some existence results for sequential neutral differential equations involving Hadamard derivatives:. D β y(1) = η ∈ R, where D α , D β are the Hadamard fractional derivatives of order 0 < α, β < 1, respectively and f , g : J × R → R are continuous functions, J ⊆ R and φ ∈ C ([1 − r, 1], R). We cover the multivalued case of problem (1) and investigate the Hadamard type neutral fractional differential inclusions given by.
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