On Existence and Continuity Results of Solution for Multi-time Scale Fractional Stochastic Differential Equation

Alkhazzan A., Wang J., Tunç C., Ding X., Yuan Z., Nie Y.

Qualitative Theory of Dynamical Systems, vol.22, no.2, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 22 Issue: 2
  • Publication Date: 2023
  • Doi Number: 10.1007/s12346-023-00750-x
  • Journal Name: Qualitative Theory of Dynamical Systems
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
  • Keywords: Ulam-Hyers stability, Stochastic differential equations, Existence, Uniqueness, Continuity of solution, Riemann Liouville's fractional integral
  • Van Yüzüncü Yıl University Affiliated: Yes


© 2023, The Author(s), under exclusive licence to Springer Nature Switzerland AG.In this paper, we study four critical aspects of a new class of multi-time scale nonlinear fractional stochastic differential equations with fractional integral in the sense of Riemann Liouville. A primary goal of this paper is to investigate the existence, uniqueness, Ulam-Hyers stability, and continuity of the solutions under sufficient assumptions using the Banach contraction theorem. At the end of the paper, a specific example is provided to demonstrate the efficiency and effectiveness of the new results of this paper.