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- W4384208032 abstract "In the present study, we consider a time-fractional stochastic backward parabolic equation driven by standard Brownian motion. In this problem, the fractional derivative is considered in the Caputo sense. Using the minimization of a least-squares functional, stochastic variational formulation, Fréchet differentiability and utility theorems adopted directly from deterministic fractional backward equations, the existence and uniqueness theorems for a quasi solution of the proposed problem are proved. To approximate the quasi solution, a numerical technique based on 2D Chebyshev wavelets is applied. We employ the Levenberg–Marquardt regularization technique since the derived equivalent system of linear equations is ill-posed. Also, the convergence analysis for this numerical algorithm is investigated. Our results provide a new insight to find quasi solutions and apply adapted deterministic methods for some fractional stochastic backward equations. Moreover, a numerical example is provided to indicate the accuracy and efficiency of the Chebyshev wavelet method in solving the mentioned problem." @default.
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- W4384208032 date "2024-02-01" @default.
- W4384208032 modified "2023-09-29" @default.
- W4384208032 title "A numerical solution for a quasi solution of the time-fractional stochastic backward parabolic equation" @default.
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- W4384208032 doi "https://doi.org/10.1016/j.cam.2023.115441" @default.
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