INVERSE SOURCE PROBLEM FOR A SPACE-TIME FRACTIONAL DIFFUSION EQUATION

被引：26
|
作者：
Ali, Muhammad [1 ]
Aziz, Sara [1 ]
Malik, Salman A. [1 ]
机构：
[1] COMSATS Inst Informat Technol, Dept Math, Pk Rd, Islamabad, Pakistan
来源：
FRACTIONAL CALCULUS AND APPLIED ANALYSIS | 2018年 / 21卷 / 03期
关键词：
fractional derivative; Sturm-Liouville system; inverse problem; Mittag-Leffler function;
D O I：
10.1515/fca-2018-0045
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
For a space-time fractional diffusion equation, an inverse problem of determination of a space dependent source term along with the solution is considered. The fractional derivatives in time and space are defined in the sense of Caputo. Due to an over-specified data at final time say T, we proved that there exists a unique solution of the inverse source problem. We use the eigenfunction expansion method to prove our main results. Several special cases of space-time fractional diffusion equations are discussed and results are interpolated from generalized results. Some examples are provided.
引用
收藏
页码：844 / 863
页数：20
相关论文
共 50 条
  • [1] Inverse source problem for a space-time fractional diffusion equation
    Mohamed BenSaleh
    Hassine Maatoug
    [J]. Ricerche di Matematica, 2024, 73 : 681 - 713
  • [2] Inverse source problem for a space-time fractional diffusion equation
    BenSaleh, Mohamed
    Maatoug, Hassine
    [J]. RICERCHE DI MATEMATICA, 2024, 73 (02) : 681 - 713
  • [3] INverse Source Problem for a Space-Time Fractional Diffusion Equation
    Muhammad Ali
    Sara Aziz
    Salman A. Malik
    [J]. Fractional Calculus and Applied Analysis, 2018, 21 : 844 - 863
  • [4] FOURIER TRUNCATION METHOD FOR AN INVERSE SOURCE PROBLEM FOR SPACE-TIME FRACTIONAL DIFFUSION EQUATION
    Nguyen Huy Tuan
    Le Dinh Long
    [J]. ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2017,
  • [5] An inverse source problem for a one-dimensional space-time fractional diffusion equation
    Tatar, Salih
    Ulusoy, Suleyman
    [J]. APPLICABLE ANALYSIS, 2015, 94 (11) : 2233 - 2244
  • [6] Harnack's inequality for a space-time fractional diffusion equation and applications to an inverse source problem
    Jia, Junxiong
    Peng, Jigen
    Yang, Jiaqing
    [J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2017, 262 (08) : 4415 - 4450
  • [7] A UNIQUENESS RESULT FOR AN INVERSE PROBLEM IN A SPACE-TIME FRACTIONAL DIFFUSION EQUATION
    Tatar, Salih
    Ulusoy, Suleyman
    [J]. ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2013,
  • [8] An Inverse Source Problem of Space-Fractional Diffusion Equation
    Liu, Songshu
    Feng, Lixin
    Zhang, Guilai
    [J]. BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, 2021, 44 (06) : 4405 - 4424
  • [9] An Inverse Source Problem of Space-Fractional Diffusion Equation
    Songshu Liu
    Lixin Feng
    Guilai Zhang
    [J]. Bulletin of the Malaysian Mathematical Sciences Society, 2021, 44 : 4405 - 4424
  • [10] Inverse source problems for a space-time fractional differential equation
    Ali, Muhammad
    Aziz, Sara
    Malik, Salman A.
    [J]. INVERSE PROBLEMS IN SCIENCE AND ENGINEERING, 2020, 28 (01) : 47 - 68
12345