Existence Theory and Ulam’s Stabilities of Fractional Langevin Equation

Rizwan, Rizwan ^[2] ; Zada, Akbar ^[1]
1. [1] University of Peshawar
  
  University of Peshawar
  
  Pakistán
2. [2] University of Buner
Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 20, Nº 2, 2021
Idioma: inglés
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Resumen
- 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.