New techniques for the existence and stability of solutions to fractional stochastic pantograph differential equations
Boundary Value Problems, vol.2026, no.1, 2026 (SCI-Expanded, Scopus)
- 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.