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

Yıl 2024, Cilt: 7 Sayı: 2, 88 - 103

Ayoub Louakar Ahmed Kajounı Khalid Hilal Hamid Lmou

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

Öz

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.

Anahtar Kelimeler

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

Etik Beyan

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

Destekleyen Kurum

No funding supporting.

Proje Numarası

1

Teşekkür

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

Kaynakça

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