Existence Theory and Ulam’s Stabilities of Fractional Langevin Equation

In this paper, we consider fractional Langevin equation and derive a formula of solutions for fractional Langevin equation involving two Caputo fractional derivatives. Secondly, we implement the concept of Ulam–Hyers as well as Ulam–Hyers–Rassias stability. Then, we choose Generalized Diaz–Margolis’...

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Bibliographic Details
Published inQualitative theory of dynamical systems Vol. 20; no. 2
Main Authors Rizwan, Rizwan, Zada, Akbar
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.07.2021
Springer Nature B.V
Subjects
Difference and Functional Equations
Dynamical Systems and Ergodic Theory
Mathematics
Mathematics and Statistics
Metric space
Stability
Langevin Equation
34B27
Fixed point theorem
Caputo derivative
Ulam–Hyers–Rassias stability
26A33
Ulam–Hyers stability
34A08
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Summary:In this paper, we consider fractional Langevin equation and derive a formula of solutions for fractional Langevin equation involving two Caputo fractional derivatives. Secondly, we implement the concept of Ulam–Hyers as well as Ulam–Hyers–Rassias stability. Then, we choose Generalized Diaz–Margolis’s fixed point approach to derive Ulam–Hyers as well as Ulam–Hyers–Rassias stability results for our proposed model, over generalized complete metric space. We give several examples which support our main results.
ISSN:1575-5460
1662-3592
DOI:10.1007/s12346-021-00495-5