Approximate solutions for neutral stochastic fractional differential equations

This study focuses on a class of neutral stochastic fractional differential equations of order α∈(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 Bana...

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Bibliographic Details
Published in:Communications in nonlinear science & numerical simulation 2023-10, Vol.125, p.107414, Article 107414
Main Authors: Khatoon, A., Raheem, A., Afreen, A.
Format: Article
Language:English
Subjects:
Analytic semi group
Caputo derivative
Cosine family
Faedo–Galerkin approximation
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Summary:This study focuses on a class of neutral stochastic fractional differential equations of order α∈(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. •We consider a class of neutral stochastic fractional differential equation of order α∈(1,2] in a separable Hilbert space.•We use the projection operator to restrict our main problem on a finite-dimensional subspace.•The theory of the cosine family and fractional powers of a closed linear operator, stochastic analysis techniques, and the Banach contraction principle are used.•Faedo–Galerkin approximations are used to demonstrate the convergence of approximate solutions.
ISSN:1007-5704
DOI:10.1016/j.cnsns.2023.107414