Proceedings of the International Academic Summer Conference on Number Theory and Information Security (NTIS 2023)

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A Comprehensive Study on Existence theory and Ulam’s stabilities of Impulsive Fractional Langevin Equation

Authors
Rizwan Rizwan1, *, Fengxia Liu1, Akbar Zada1, Syed Omar Shah1
1School of Interdisciplinary Studies, Renmin University of China, Beijing, P. R. China
*Corresponding author. Email: rizwan@ruc.edu.cn
Corresponding Author
Rizwan Rizwan
Available Online 2 August 2024.
DOI
10.2991/978-94-6463-463-1_3How to use a DOI?
Keywords
Langevin equation; Mittag-Leffler functions; fractional derivative; stability
Abstract

In this paper, a class of impulsive fractional Langevin equation is considered and proceeds to derive a solution formula for this equation, incorporating Mittag-Leffler functions. The solution is obtained through an analysis of linear Langevin equation involving distinct fractional derivatives. We establish the existence and uniqueness results of the solution by employing mathematical tools such as boundedness, continuity, monotonicity, and non-negativity properties of Mittag-Leffler functions and fixed point methods. Furthermore, we establish appropriate conditions and results to discuss Ulam–Hyers, generalized Ulam–Hyers, Ulam–Hyers–Rassias and generalized Ulam–Hyers–Rassias stability of our proposed model, with the help of fixed point theorem. Finally, the theoretical findings are illustrated through a practical example.

Copyright
© 2024 The Author(s)
Open Access
Open Access This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/), which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

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Volume Title
Proceedings of the International Academic Summer Conference on Number Theory and Information Security (NTIS 2023)
Series
Advances in Physics Research
Publication Date
2 August 2024
ISBN
978-94-6463-463-1
ISSN
2352-541X
DOI
10.2991/978-94-6463-463-1_3How to use a DOI?
Copyright
© 2024 The Author(s)
Open Access
Open Access This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/), which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

Cite this article

risenwbib
TY  - CONF
AU  - Rizwan Rizwan
AU  - Fengxia Liu
AU  - Akbar Zada
AU  - Syed Omar Shah
PY  - 2024
DA  - 2024/08/02
TI  - A Comprehensive Study on Existence theory and Ulam’s stabilities of Impulsive Fractional Langevin Equation
BT  - Proceedings of the International Academic Summer Conference on Number Theory and Information Security (NTIS 2023)
PB  - Atlantis Press
SP  - 22
EP  - 51
SN  - 2352-541X
UR  - https://doi.org/10.2991/978-94-6463-463-1_3
DO  - 10.2991/978-94-6463-463-1_3
ID  - Rizwan2024
ER  -