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

Author

Listed:
  • Ali Rezaiguia

    (Department of Mathematics, College of Science, University of Hail, Hail 2440, Saudi Arabia
    Department of Computer Science and Mathematics, Mouhamed Cherif Messadia University, Souk Ahras BP 1553, Algeria)

  • Taher S. Hassan

    (Department of Mathematics, College of Science, University of Hail, Hail 2440, Saudi Arabia
    Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt)

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.

Suggested Citation

  • Ali Rezaiguia & Taher S. Hassan, 2023. "Topological Structure and Existence of Solutions Set for q-Fractional Differential Inclusion in Banach Space," Mathematics, MDPI, vol. 11(3), pages 1-9, January.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:3:p:683-:d:1050293
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    References listed on IDEAS

    as
    1. Mabrouk Bragdi & Amar Debbouche & Dumitru Baleanu, 2013. "Existence of Solutions for Fractional Differential Inclusions with Separated Boundary Conditions in Banach Space," Advances in Mathematical Physics, Hindawi, vol. 2013, pages 1-5, May.
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