Some results on proportional Caputo neutral fractional stochastic differential equations. (English) Zbl 07920741
Summary: This paper explores Proportional Neutral Fractional Stochastic Differential Equations (PNFSDEs), emphasizing their existence, uniqueness, and Hyers-Ulam Stability (HUS). The continuous dependence of solutions on initial data and their regularity in time are also established. By using the Banach Fixed Point Theorem (BFPT), Itô’s isometry formula, and some classical inequalities, we obtain the theoretical findings. Finally, we present an example to illustrate the effectiveness of our results.
MSC:
| 34K50 | Stochastic functional-differential equations |
| 34K40 | Neutral functional-differential equations |
| 34K37 | Functional-differential equations with fractional derivatives |
Keywords:
existence and uniqueness; Ulam-Hyers stability; proportional fractional derivative; stochastic neutral differential equationReferences:
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