Topological Structure and Existence of Solutions Set for q-Fractional Differential Inclusion in Banach Space

Ali Rezaiguia () and Taher S. Hassan
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Ali Rezaiguia: Department of Mathematics, College of Science, University of Hail, Hail 2440, Saudi Arabia
Taher S. Hassan: Department of Mathematics, College of Science, University of Hail, Hail 2440, Saudi Arabia

Mathematics, 2023, vol. 11, issue 3, 1-9

Abstract: In this work, we concentrate on the existence of the solutions set of the following problem c D q α σ ( t ) ∈ F ( t , σ ( t ) , c D q α σ ( t ) ) , t ∈ I = [ 0 , T ] σ 0 = σ 0 ∈ E , as well as its topological structure in Banach space E . By transforming the problem posed into a fixed point problem, we provide the necessary conditions for the existence and compactness of solutions set. Finally, we present an example as an illustration of main results.

Keywords: Caputo fractional q-difference inclusion; measure of non-compactness; Darbo point theorem; selection theory (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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