A Class of Implicit Fractional $\psi$-Hilfer Langevin Equation with Time Delay and Impulse in the Weighted Space

Year 2024, Volume: 7 Issue: 2, 88 - 103, 30.06.2024

Ayoub Louakar , Ahmed Kajounı , Khalid Hilal , Hamid Lmou

https://doi.org/10.33434/cams.1425019

Abstract

In this paper, the Ulam-Hyers-Rassias stability is discussed and the existence and uniqueness of solutions for a class of implicit fractional $\psi$-Hilfer Langevin equation with impulse and time delay are investigated. A novel form of generalized Gronwall inequality is introduced. Picard operator theory is employed in authour’s analysis. An example will be given to support the validity of our findings.

Keywords

Existence and uniqueness, Generalized Gronwall inequality, $\psi$-Hilfer Langevin equation, Picard operator theory, Ulam-Hyers-Rassias stability

Ethical Statement

There are no conflicts of interest, according to the authors.

Supporting Institution

No funding supporting.

Project Number

1

Thanks

The authors appreciate the referee's thoughtful comments on the manuscript, which helped to improve it.

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