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Boundary Value Problem for the Langevin Equation and Inclusion with the Hilfer Fractional Derivative

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  • Khalid Hilal
  • Ahmed Kajouni
  • Hamid Lmou
  • Gaston Mandata Ngurkata

Abstract

In this work, we discuss the existence and uniqueness of solution for a boundary value problem for the Langevin equation and inclusion with the Hilfer fractional derivative. First of all, we give some definitions, theorems, and lemmas that are necessary for the understanding of the manuscript. Second of all, we give our first existence result, based on Krasnoselskii’s fixed point, and to deal with the uniqueness result, we use Banach’s contraction principle. Third of all, in the inclusion case, to obtain the existence result, we use the Leray–Schauder alternative. Last but not least, we give an illustrative example.

Suggested Citation

  • Khalid Hilal & Ahmed Kajouni & Hamid Lmou & Gaston Mandata Ngurkata, 2022. "Boundary Value Problem for the Langevin Equation and Inclusion with the Hilfer Fractional Derivative," International Journal of Differential Equations, Hindawi, vol. 2022, pages 1-12, March.
    • Handle: RePEc:hin:jnijde:3386198
    DOI: 10.1155/2022/3386198
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