Progress in Fractional Differentiation & Applications

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In this paper, we study a general time-fractional diffusion equation involving the Atangana-Baleanu derivative of Caputo sense. First, we derive weak maximum-minimum principles to the associated fractional differential operators of the parabolic type, then we apply these principles to establish uniqueness and stability results to initial-boundary value problem and to obtain a norm estimate of the solution. For the existence of solution to the problem, we apply the eigenfunction expansion method to construct a formal solution, which under certain conditions proved to be a weak solution.

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