New techniques for the existence and stability of solutions to fractional stochastic pantograph differential equations

Khan R. U., ABDELJAWAD T., Abdalla B.

Boundary Value Problems, vol.2026, no.1, 2026 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 2026 Issue: 1
  • Publication Date: 2026
  • Doi Number: 10.1186/s13661-025-02187-4
  • Journal Name: Boundary Value Problems
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, Directory of Open Access Journals
  • Keywords: Caputo fractional derivative, Fixed point theorems, Fractional stochastic differential equation, Stability
  • Istanbul Gelisim University Affiliated: Yes

Abstract

In this work, we study the existence, uniqueness, and stability of fractional stochastic pantograph differential equations involving the Caputo fractional derivative. By applying a fixed-point theorem under suitable assumptions, we establish sufficient conditions for the existence and uniqueness of solutions to the proposed equations. Additionally, we prove that the solution is Hyers-Ulam stable. Our results also provide a significant generalization of existing findings in the literature. Finally, a concrete example is presented to illustrate the effectiveness of the obtained results.