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A New Result for ψ-Hilfer Fractional Pantograph-Type Langevin Equation and Inclusions

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  • Hamid Lmou
  • Khalid Hilal
  • Ahmed Kajouni
  • Serkan Araci

Abstract

In this paper, we deal with the existence and uniqueness of solution for ψ-Hilfer Langevin fractional pantograph differential equation and inclusion; these types of pantograph equations are a special class of delay differential equations. The existence and uniqueness results are obtained by making use of the Krasnoselskii fixed-point theorem and Banach contraction principle, and for the inclusion version, we use the Martelli fixed-point theorem to get the existence result. In the end, we are giving an example to illustrate our results.

Suggested Citation

  • Hamid Lmou & Khalid Hilal & Ahmed Kajouni & Serkan Araci, 2022. "A New Result for ψ-Hilfer Fractional Pantograph-Type Langevin Equation and Inclusions," Journal of Mathematics, Hindawi, vol. 2022, pages 1-10, September.
    • Handle: RePEc:hin:jjmath:2441628
    DOI: 10.1155/2022/2441628
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