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Nonlocal Conformable-Fractional Differential Equations with a Measure of Noncompactness in Banach Spaces

Author

Listed:
  • Mohamed Bouaouid
  • Mohamed Hannabou
  • Khalid Hilal
  • Nasser Saad

Abstract

This paper deals with the existence of mild solutions for the following Cauchy problem: dαxt/dtα=Axt+ft,xt,x0=x0+gx,t∈0,τ, where dα./dtα is the so-called conformable fractional derivative. The linear part A is the infinitesimal generator of a uniformly continuous semigroup Ttt≥0 on a Banach space X, f and g are given functions. The main result is proved by using the Darbo–Sadovskii fixed point theorem without assuming the compactness of the family Ttt>0 and the Lipshitz condition on the nonlocal part g.

Suggested Citation

  • Mohamed Bouaouid & Mohamed Hannabou & Khalid Hilal & Nasser Saad, 2020. "Nonlocal Conformable-Fractional Differential Equations with a Measure of Noncompactness in Banach Spaces," Journal of Mathematics, Hindawi, vol. 2020, pages 1-6, February.
    • Handle: RePEc:hin:jjmath:5615080
    DOI: 10.1155/2020/5615080
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    Cited by:

    1. Sivajiganesan Sivasankar & Ramalingam Udhayakumar & Muchenedi Hari Kishor & Sharifah E. Alhazmi & Shrideh Al-Omari, 2022. "A New Result Concerning Nonlocal Controllability of Hilfer Fractional Stochastic Differential Equations via almost Sectorial Operators," Mathematics, MDPI, vol. 11(1), pages 1-18, December.

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