Quasi Solution of an Inverse Fractional Stochastic Nonlinear Partial Differential Equation of Parabolic Type

doi:10.1007/s42967-023-00319-0

Communications on Applied Mathematics and Computation ›› 2025, Vol. 7 ›› Issue (4): 1350-1363.doi: 10.1007/s42967-023-00319-0

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Quasi Solution of an Inverse Fractional Stochastic Nonlinear Partial Differential Equation of Parabolic Type

T. Nasiri, A. Zakeri, A. Aminataei

Faculty of Mathematics, K. N. Toosi University of Technology, Tehran, Iran

收稿日期:2023-01-16 修回日期:2023-06-20 接受日期:2023-09-14 出版日期:2023-12-26 发布日期:2023-12-26
通讯作者: A.Zakeri,E-mail:azakeri@kntu.ac.ir E-mail:azakeri@kntu.ac.ir
作者简介:T.Nasiri, E-mail:t_nasiri@email.kntu.ac.ir;A.Aminataei, E-mail:ataei@kntu.ac.ir
基金资助:
The authors declare that no funds, grants, or other support was received during the preparation of this manuscript.

Quasi Solution of an Inverse Fractional Stochastic Nonlinear Partial Differential Equation of Parabolic Type

T. Nasiri, A. Zakeri, A. Aminataei

Faculty of Mathematics, K. N. Toosi University of Technology, Tehran, Iran

Received:2023-01-16 Revised:2023-06-20 Accepted:2023-09-14 Online:2023-12-26 Published:2023-12-26
Supported by:
The authors declare that no funds, grants, or other support was received during the preparation of this manuscript.

摘要/Abstract

摘要： In this paper, the existence theorem for a quasi solution of an inverse fractional stochastic parabolic equation driven by multiplicative noise in the form ^cD^α_tu-div(g(x,▽u))=f(x,u)+σ(x,u)ẇ(t) is given. In this equation, the fractional derivative is considered in the Caputo sense. Also, the random function g is unknown and should be determined. To identify the unknown coefficient, the minimization and stochastic variational formulation methods in a fractional stochastic Sobolev space are used. Indeed, we obtain a stability estimation and then prove the continuity of the minimization functional using obtained stability estimation. These results show the existence of the quasi solution for the mentioned problem.

关键词: Inverse problem, Fractional differential equation, Stochastic equation, Quasi solution, Multiplicative noise, Caputo fractional derivative

Abstract: In this paper, the existence theorem for a quasi solution of an inverse fractional stochastic parabolic equation driven by multiplicative noise in the form ^cD^α_tu-div(g(x,▽u))=f(x,u)+σ(x,u)ẇ(t) is given. In this equation, the fractional derivative is considered in the Caputo sense. Also, the random function g is unknown and should be determined. To identify the unknown coefficient, the minimization and stochastic variational formulation methods in a fractional stochastic Sobolev space are used. Indeed, we obtain a stability estimation and then prove the continuity of the minimization functional using obtained stability estimation. These results show the existence of the quasi solution for the mentioned problem.

Key words: Inverse problem, Fractional differential equation, Stochastic equation, Quasi solution, Multiplicative noise, Caputo fractional derivative

中图分类号:

T. Nasiri, A. Zakeri, A. Aminataei. Quasi Solution of an Inverse Fractional Stochastic Nonlinear Partial Differential Equation of Parabolic Type[J]. Communications on Applied Mathematics and Computation, 2025, 7(4): 1350-1363.

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Quasi Solution of an Inverse Fractional Stochastic Nonlinear Partial Differential Equation of Parabolic Type

Quasi Solution of an Inverse Fractional Stochastic Nonlinear Partial Differential Equation of Parabolic Type

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