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Fractional q -Difference Inclusions in Banach Spaces

Author

Listed:
  • Badr Alqahtani

    (Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia)

  • Saïd Abbas

    (Department of Mathematics, Tahar Moulay University of Saïda, P.O. Box 138, EN-Nasr, 20000 Saïda, Algeria)

  • Mouffak Benchohra

    (Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
    Laboratory of Mathematics, Djillali Liabes University of Sidi Bel-Abbès, P.O. Box 89, 22000 Sidi Bel-Abbès, Algeria)

  • Sara Salem Alzaid

    (Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia)

Abstract

In this paper, we study a class of Caputo fractional q-difference inclusions in Banach spaces. We obtain some existence results by using the set-valued analysis, the measure of noncompactness, and the fixed point theory (Darbo and Mönch’s fixed point theorems). Finally we give an illustrative example in the last section. We initiate the study of fractional q -difference inclusions on infinite dimensional Banach spaces.

Suggested Citation

  • Badr Alqahtani & Saïd Abbas & Mouffak Benchohra & Sara Salem Alzaid, 2020. "Fractional q -Difference Inclusions in Banach Spaces," Mathematics, MDPI, vol. 8(1), pages 1-12, January.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:1:p:91-:d:305706
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    References listed on IDEAS

    as
    1. Sina Etemad & Sotiris K. Ntouyas & Bashir Ahmad, 2019. "Existence Theory for a Fractional q -Integro-Difference Equation with q -Integral Boundary Conditions of Different Orders," Mathematics, MDPI, vol. 7(8), pages 1-15, July.
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