Regularization of the Time-Fractional Order SchröDinger Problem by Using the Mollification Regularization Method

被引：0
|
作者：
Yang, Lan [1 ]
Zhu, Lin [1 ]
He, Shangqin [2 ]
Zhao, Bingxin [1 ]
机构：
[1] Ningxia Univ, Ningxia Basic Sci Res Ctr Math, Sch Math & Stat, Ningxia Key Lab Interdisciplinary Mech & Sci Comp, Yinchuan, Peoples R China
[2] North Minzu Univ, Sch Math & Informat Sci, Yinchuan, Peoples R China
来源：
MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2025年 / 48卷 / 06期
基金：
美国国家科学基金会;
关键词：
a posteriori selection rule; a Dirichlet kernel; ill-posed problem; inverse time-fractional Schr & ouml; dinger problem; mollification regularization method; SCHRODINGER-EQUATION;
D O I：
10.1002/mma.10716
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This study investigates the solution of an ill-posed time-fractional order Schr & ouml;dinger equation using a mollification regularization technique of the Dirichlet kernel. The Dirichlet regularized solution is obtained through convolution of the Dirichlet kernel with real measured data. Estimations of convergence are derived based on parameter selection criteria of a priori and a posteriori. The efficiency of the methodology was successfully verified by simulation tests.
引用
收藏
页码：6799 / 6817
页数：19
相关论文
共 50 条
  • [21] A new regularization for time-fractional backward heat conduction problem
    Nair, M. Thamban
    Danumjaya, P.
    JOURNAL OF INVERSE AND ILL-POSED PROBLEMS, 2024, 32 (01): : 41 - 56
  • [22] Regularization of a backward problem for the inhomogeneous time-fractional wave equation
    Huy Tuan, Nguyen
    Au, Vo
    Nhat Huynh, Le
    Zhou, Yong
    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2020, 43 (08) : 5450 - 5463
  • [23] Fractional Landweber Iterative Regularization Method for Identifying the Unknown Source of the Time-Fractional Diffusion Problem
    Fan Yang
    Jun-Liang Fu
    Ping Fan
    Xiao-Xiao Li
    Acta Applicandae Mathematicae, 2021, 175
  • [24] Regularization of the Final Value Problem for the Time-Fractional Diffusion Equation
    Al-Jamal, Mohammad F.
    Barghout, Kamal
    Abu-Libdeh, Nidal
    IRANIAN JOURNAL OF SCIENCE, 2023, 47 (03) : 931 - 941
  • [25] Fourier regularization for a final value time-fractional diffusion problem
    Yang, Ming
    Liu, Jijun
    APPLICABLE ANALYSIS, 2015, 94 (07) : 1508 - 1526
  • [26] Regularization of the Final Value Problem for the Time-Fractional Diffusion Equation
    Mohammad F. Al-Jamal
    Kamal Barghout
    Nidal Abu-Libdeh
    Iranian Journal of Science, 2023, 47 : 931 - 941
  • [27] Regularization by projection for a backward problem of the time-fractional diffusion equation
    Ren, Caixuan
    Xu, Xiang
    Lu, Shuai
    JOURNAL OF INVERSE AND ILL-POSED PROBLEMS, 2014, 22 (01): : 121 - 139
  • [28] Regularization of a nonlinear inverse problem by discrete mollification method
    Bodaghi, Soheila
    Zakeri, Ali
    Amiraslani, Amir
    COMPUTATIONAL METHODS FOR DIFFERENTIAL EQUATIONS, 2021, 9 (01): : 313 - 326
  • [29] A mollification regularization method for identifying the time-dependent heat source problem
    Fan Yang
    Chu-Li Fu
    Xiao-Xiao Li
    Journal of Engineering Mathematics, 2016, 100 : 67 - 80
  • [30] An inverse problem for an inhomogeneous time-fractional diffusion equation: a regularization method and error estimate
    Nguyen Huy Tuan
    Luu Vu Cam Hoan
    Salih Tatar
    Computational and Applied Mathematics, 2019, 38
12345