Existence, uniqueness and Ulam’s stabilities for a class of impulsive Langevin equation with Hilfer fractional derivatives
- Authors
- Rizwan, Rizwan; Lee, Jung Rye; Park, Choonkil; Zada, Akbar
- Issue Date
- Jan-2022
- Publisher
- American Institute of Mathematical Sciences
- Keywords
- Hilfer fractional derivative; Impulse; Langevin equation; Ulam-Hyers stability
- Citation
- AIMS Mathematics, v.7, no.4, pp.6204 - 6217
- Indexed
- SCIE
SCOPUS
- Journal Title
- AIMS Mathematics
- Volume
- 7
- Number
- 4
- Start Page
- 6204
- End Page
- 6217
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/139857
- DOI
- 10.3934/math.2022345
- ISSN
- 2473-6988
- Abstract
- In this manuscript, a class of impulsive Langevin equation with Hilfer fractional derivatives is considered. Using the techniques of nonlinear functional analysis, we establish appropriate conditions and results to discuss existence, uniqueness and different types of Ulam-Hyers stability results of our proposed model, with the help of Banach’s fixed point theorem. An example is provided at the end to illustrate our results.
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