Recovering source term and temperature distribution for nonlocal heat equation. (English) Zbl 07689963
Summary: We consider two problems of recovering the source terms along with heat concentration for a time fractional heat equation involving the so-called \(m\) th level fractional derivative (LFD) (proposed in a paper by Y. Luchko [Fract. Calc. Appl. Anal. 23, No. 4, 939–966 (2020; Zbl 1474.26024)]) in time variable of order between 0 and 1. The solutions of both problems are obtained by using eigenfunction expansion method. The series solutions of the inverse problems are proved to be unique and regular. The ill-posedness of inverse problems is proved in the sense of Hadamard and some numerical examples are presented.
MSC:
| 65L05 | Numerical methods for initial value problems involving ordinary differential equations |
| 34A08 | Fractional ordinary differential equations |
| 65L60 | Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations |
Citations:
Zbl 1474.26024References:
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