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An inverse coefficient-source problem for a time-fractional diffusion equation

Loubna Settara, Rahima Atmania

Abstract



In this paper, a unique solution to an inverse source problem for a one-dimensional time-fractional diffusion equation is obtained as a convergent series. This existence and uniqueness result is based on the Fourier method, the fractional calculus and the Banach fixed point principle. The unknown
source coefficient is determined uniquely by the additional data which is an integral condition. Then, the continuous dependence of data is proved.

Keywords


Time-fractional diffusion equation, fractional derivative, inverse problem, bi-orthogonal system of functions, Fourier series, Banach fixed point theorem.

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