The fractional Dodson diffusion equation: a new approach

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 fun...

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Bibliographic Details
Published in:Ricerche di matematica 2018-11, Vol.67 (2), p.899-909
Main Authors: Garra, Roberto, Giusti, Andrea, Mainardi, Francesco
Format: Article
Language:English
Subjects:
Algebra
Analysis
Geometry
Mathematics
Mathematics and Statistics
Nonlinear equations
Numerical Analysis
Probability Theory and Stochastic Processes
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Summary: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.
ISSN:0035-5038
1827-3491
DOI:10.1007/s11587-018-0354-3