Determination of unknown source term and boundary flux in a time-fractional inverse diffusion problem

Document Type : Original Paper


1 1 Department of Mathematics, Khuzestan Science and Research Branch, Islamic Azad University, Ahvaz, Iran, 2 Department of Mathematics, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran.

2 School of Mathematics, Iran University of Science and Technology, Tehran, Iran

3 Department of Mathematics, Payame Noor University, Tehran, Iran


In this work, we consider an inverse fractional parabolic problem that has many applications in different fields. Simultaneously determination of a source term and a boundary flux function in a time-fractional order parabolic equation is investigated using a mollified space marching method. Superposition and Duhamel's principles, the uniqueness of solution with respect to an over determination condition is proved. The stability and convergence of the numerical method are proved and two numerical test problems are conducted to illustrate the ability and accuracy of the numerical method.


Main Subjects

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Volume 11, Issue 2
June 2021
Pages 271-287
  • Receive Date: 05 October 2020
  • Revise Date: 09 March 2021
  • Accept Date: 27 March 2021
  • First Publish Date: 11 May 2021