In this paper, a time-fractional diffusion equation of distributed order including the Caputo-Prabhakar fractional derivative is studied. We use a numerical method based on the linear B-spline interpolation and finite difference method to study the solutions of these types of fractional equations. Finally, some numerical examples are presented for the performance and accuracy of the proposed numerical method.

Keywords: Fractional derivative, Distributed order time-fractional diffusion equation, Distributed order, Caputo-Prabhakar, Spline approximation

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