Abstract
ABSTRACTIn this paper, we consider the Mittag-Leffler operator as an analytical solution of time-fractional diffusion equation in the Caputo sense. This solution is presented by an integral representation in terms of the M-Wright functions and the exponential operators. Further, we study the Mittag-Leffler operators associated with the Legendre and Bessel diffusion equations. Finally, we extend the obtained integral representation for the time-fractional diffusion equation of distributed order.
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