The fractional Dodson diffusion equation: a new approach

TL;DR

This paper introduces a novel fractional generalization of Dodson's diffusion equation, deriving its fundamental solution using the M-Wright function and exploring nonlinear variants, advancing fractional diffusion modeling techniques.

Contribution

It presents a new fractional Dodson diffusion equation and derives its fundamental solution, extending the mathematical framework for fractional diffusion processes.

Findings

Fundamental solution expressed via M-Wright function of two variables

Extension to nonlinear fractional Dodson-like equations

Provides a new approach to fractional diffusion equations

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.