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.
The fractional Dodson diffusion equation: a new approach / Garra, R.; Giusti, A.; Mainardi, F.. - In: RICERCHE DI MATEMATICA. - ISSN 0035-5038. - 67:2(2018), pp. 899-909. [10.1007/s11587-018-0354-3]
The fractional Dodson diffusion equation: a new approach
Garra R.;
2018
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
