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TERMINAL VALUE PROBLEM FOR STOCHASTIC FRACTIONAL EQUATION WITHIN AN OPERATOR WITH EXPONENTIAL KERNEL

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dc.contributor.author NGUYEN DUC PHUONG
dc.contributor.author LUU VU CAM HOAN
dc.contributor.author DUMITRU BALEANU
dc.contributor.author ANH TUAN NGUYEN
dc.date.accessioned 2024-03-07T01:45:21Z
dc.date.available 2024-03-07T01:45:21Z
dc.date.issued 2023
dc.description.abstract <jats:p>In this paper, we investigate a terminal value problem for stochastic fractional diffusion equations with Caputo–Fabrizio derivative. The stochastic noise we consider here is the white noise taken value in the Hilbert space [Formula: see text]. The main contribution is to investigate the well-posedness and ill-posedness of such problem in two distinct cases of the smoothness of the Hilbert scale space [Formula: see text] (see Assumption 3.1), which is a subspace of [Formula: see text]. When [Formula: see text] is smooth enough, i.e. the parameter [Formula: see text] is sufficiently large, our problem is well-posed and it has a unique solution in the space of Hölder continuous functions. In contract, in the different case when [Formula: see text] is smaller, our problem is ill-posed; therefore, we construct a regularization result.</jats:p>
dc.identifier.doi 10.1142/S0218348X23400625
dc.identifier.uri http://repository.vlu.edu.vn:443/handle/123456789/12871
dc.language.iso en_US
dc.relation.ispartof Fractals
dc.relation.issn 0218-348X
dc.relation.issn 1793-6543
dc.subject "Ill-Posed Problem
dc.subject Fractional Stochastic Equation
dc.subject Hilbert Scales
dc.subject Caputo–Fabrizio Derivative."
dc.title TERMINAL VALUE PROBLEM FOR STOCHASTIC FRACTIONAL EQUATION WITHIN AN OPERATOR WITH EXPONENTIAL KERNEL
dc.type journal-article
dspace.entity.type Publication
oaire.citation.issue 04
oaire.citation.volume 31
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