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

Ayoub Louakar; Ahmed Kajounı; Khalid Hilal; Hamid Lmou

doi:10.33434/cams.1425019

EN

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

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

Supporting Institution

No funding supporting.

Project Number

1

Ethical Statement

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

Thanks

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

References

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Details

Primary Language

English

Subjects

Pure Mathematics (Other)

Journal Section

Research Article

Authors

Ayoub Louakar ^*
0009-0007-1523-9291
Morocco

Ahmed Kajounı
0000-0001-8484-6107
Morocco

Khalid Hilal
0000-0002-0806-2623
Morocco

Hamid Lmou
0000-0002-8786-2230
Morocco

Early Pub Date

June 5, 2024

Publication Date

June 30, 2024

Submission Date

January 24, 2024

Acceptance Date

May 25, 2024

Published in Issue

Year 2024 Volume: 7 Number: 2

DOI

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

IZ

https://izlik.org/JA49XH36BD

APA

Louakar, A., Kajounı, A., Hilal, K., & Lmou, H. (2024). A Class of Implicit Fractional $\psi$-Hilfer Langevin Equation with Time Delay and Impulse in the Weighted Space. Communications in Advanced Mathematical Sciences, 7(2), 88-103. https://doi.org/10.33434/cams.1425019

AMA

1.Louakar A, Kajounı A, Hilal K, Lmou H. A Class of Implicit Fractional $\psi$-Hilfer Langevin Equation with Time Delay and Impulse in the Weighted Space. Communications in Advanced Mathematical Sciences. 2024;7(2):88-103. doi:10.33434/cams.1425019

Chicago

Louakar, Ayoub, Ahmed Kajounı, Khalid Hilal, and Hamid Lmou. 2024. “A Class of Implicit Fractional $\psi$-Hilfer Langevin Equation With Time Delay and Impulse in the Weighted Space”. Communications in Advanced Mathematical Sciences 7 (2): 88-103. https://doi.org/10.33434/cams.1425019.

EndNote

Louakar A, Kajounı A, Hilal K, Lmou H (June 1, 2024) A Class of Implicit Fractional $\psi$-Hilfer Langevin Equation with Time Delay and Impulse in the Weighted Space. Communications in Advanced Mathematical Sciences 7 2 88–103.

IEEE

[1]A. Louakar, A. Kajounı, K. Hilal, and H. Lmou, “A Class of Implicit Fractional $\psi$-Hilfer Langevin Equation with Time Delay and Impulse in the Weighted Space”, Communications in Advanced Mathematical Sciences, vol. 7, no. 2, pp. 88–103, June 2024, doi: 10.33434/cams.1425019.

ISNAD

Louakar, Ayoub - Kajounı, Ahmed - Hilal, Khalid - Lmou, Hamid. “A Class of Implicit Fractional $\psi$-Hilfer Langevin Equation With Time Delay and Impulse in the Weighted Space”. Communications in Advanced Mathematical Sciences 7/2 (June 1, 2024): 88-103. https://doi.org/10.33434/cams.1425019.

JAMA

1.Louakar A, Kajounı A, Hilal K, Lmou H. A Class of Implicit Fractional $\psi$-Hilfer Langevin Equation with Time Delay and Impulse in the Weighted Space. Communications in Advanced Mathematical Sciences. 2024;7:88–103.

MLA

Louakar, Ayoub, et al. “A Class of Implicit Fractional $\psi$-Hilfer Langevin Equation With Time Delay and Impulse in the Weighted Space”. Communications in Advanced Mathematical Sciences, vol. 7, no. 2, June 2024, pp. 88-103, doi:10.33434/cams.1425019.

Vancouver

1.Ayoub Louakar, Ahmed Kajounı, Khalid Hilal, Hamid Lmou. A Class of Implicit Fractional $\psi$-Hilfer Langevin Equation with Time Delay and Impulse in the Weighted Space. Communications in Advanced Mathematical Sciences. 2024 Jun. 1;7(2):88-103. doi:10.33434/cams.1425019

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Existence Results for a Class of $\psi$-Hilfer Fractional Hybrid Differential Equations

Turkish Journal of Mathematics and Computer Science

https://doi.org/10.47000/tjmcs.1491105

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