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Garra, Roberto; Giusti, Andrea; Mainardi, Francesco (2018): The fractional Dodson diffusion equation: a new approach. In: Ricerche Di Matematica, Vol. 67, No. 2: pp. 899-909
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Abstract

In this paper, after a brief review of the general theory concerning regularized derivatives and integrals of a function with respect to another function, we provide a peculiar fractional generalization of the (1 + 1)-dimensional Dodson's diffusion equation. For the latter we then compute the fundamental solution, which turns out to be expressed in terms of an M-Wright function of two variables. Then, we conclude the paper providing a few interesting results for some nonlinear fractional Dodson-like equations.