Inverse source problem for a fractional diffusion equation

An inverse source problem for a fractional diffusion equation is investigated. Under an assumption that the unknown source term is time independent, an analytical solution can be deduced based on the method of the eigenfunction expansion. Then, the uniqueness of the inverse problem is proved by analytic continuation and Laplace transform. Regularization schemes are considered to obtain the regularized solution. Numerical examples are presented to illustrate the validity and effectiveness of the proposed meshless method.

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