Approximate solutions for neutral stochastic fractional differential equations. (English) Zbl 1518.34083
Summary: This study focuses on a class of neutral stochastic fractional differential equations of order \(\alpha\in(1,2]\) in a separable Hilbert space. The existence and uniqueness of approximate solutions are demonstrated using semigroup theory of bounded linear operators, stochastic analysis techniques, and the Banach contraction principle. The convergence of approximate solutions is illustrated using Faedo-Galerkin approximations. Finally, we give an example to illustrate the abstract results.
MSC:
| 34K37 | Functional-differential equations with fractional derivatives |
| 46C15 | Characterizations of Hilbert spaces |
| 60H15 | Stochastic partial differential equations (aspects of stochastic analysis) |
| 47N20 | Applications of operator theory to differential and integral equations |
| 35R11 | Fractional partial differential equations |
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