An inverse source time-fractional diffusion problem via an input-output mapping


  • Rahima Atmania University of Badji Mokhtar Annaba.
  • Loubna Settara University of 20 august 1955.



inverse source problem, time-fractional diffusion equation, Riemann-Liouville fractional derivative, input-output mapping, distinguishability


In this paper, we investigate an inverse source problem involving a one-dimensional diffusion equation of a time-fractional RiemannLiouville derivative with 0 < α < 1. First, results on the existence and regularity of the weak solution of the direct problem are obtained. For the determination of the unknown time-dependent source term, we use a monotone and distinguishable input-output mapping defined by the additional over-determination integral data for the considered sub-diffusion problem. Finally, the uniqueness of the solution of the inverse problem is proved.

Author Biographies

Rahima Atmania, University of Badji Mokhtar Annaba.

Applied Mathematics Laboratory, Department of Mathematics, Faculty of Sciences.

Loubna Settara, University of 20 august 1955.

Lamahis Laboratory, Departement of Mathematics.


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How to Cite

R. Atmania and L. Settara, “An inverse source time-fractional diffusion problem via an input-output mapping”, Proyecciones (Antofagasta, On line), vol. 42, no. 5, pp. 1105-1127, Sep. 2023.