Ulam-Hyers stability of Caputo-type fractional fuzzy stochastic differential equations with delay. (English) Zbl 1517.34105
Summary: We explore a new kind of Caputo-type fractional fuzzy stochastic differential equations (FFSDEs) with delay. We establish the existence result of FFSDEs with delay by monotone iterative technique combined with the method of upper and lower solutions, and then the uniqueness is proved. Subsequently, we study the Ulam-Hyers (U-H) stability. Finally, three examples with numerical simulations are provided to illustrate the theoretical results.
MSC:
| 34K37 | Functional-differential equations with fractional derivatives |
| 34K36 | Fuzzy functional-differential equations |
| 34K50 | Stochastic functional-differential equations |
| 34K27 | Perturbations of functional-differential equations |
| 34K07 | Theoretical approximation of solutions to functional-differential equations |
Keywords:
fuzzy stochastic differential equations; fractional calculus; Ulam-Hyers stability; existence and uniquenessReferences:
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