Abstract
In this paper, we investigate the existence of solutions for the random fractional differential equations (RFDEs) with delay by employing Banach and Schaefer’s fixed point theorems. In addition, we present the Hyers–Ulam stability (HUS) and Hyers–Ulam–Rassias stability (HURS) for RFDEs with delay through using Gronwall inequality. Two examples are given to visualize theoretical results.
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The authors would like to express their gratitude to the anonymous referees for their helpful comments and suggestions, which have greatly improved the paper.
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Communicated by Vasily E. Tarasov.
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Vu, H., Van Hoa, N. Hyers–Ulam stability of random functional differential equation involving fractional-order derivative. Comp. Appl. Math. 41, 204 (2022). https://doi.org/10.1007/s40314-022-01915-1
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DOI: https://doi.org/10.1007/s40314-022-01915-1
Keywords
- Mean square calculus
- Stochastic fractional calculus operators
- Hyers–Ulam stability
- Stochastic differential equations