The fractional Dodson diffusion equation: a new approach

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.

10 pages, 3 figures

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• Subdiffusion equation with Caputo fractional derivative with respect to another function
• Subdiffusion equation with fractional Caputo time derivative with respect to another function in modeling transition from ordinary subdiffusion to superdiffusion
• Stochastic foundations of $g$-subdiffusion process
• On G-fractional diffusion models in bounded domains
• Existence and uniqueness of mild solutions for a class of psi-Caputo time-fractional systems of order from one to two