Generalized special functions in the description of fractional diffusive equations

Clemente Cesarano

doi:10.1515/caim-2019-0010

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Generalized special functions in the description of fractional diffusive equations

Communications in Applied and Industrial Mathematics

Volume 10 (2019): Issue 1 (February 2019)

By: Clemente Cesarano

Open Access

|Feb 2019

Abstract

Starting from the heat equation, we discuss some fractional generalizations of various forms. We propose a method useful for analytic or numerical solutions. By using Hermite polynomials of higher and fractional order, we present some operational techniques to find general solutions of extended form to d'Alembert and Fourier equations. We also show that the solutions of the generalized equations discussed here can be expressed in terms of Hermite-based functions.

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Articles in this issue

DOI: https://doi.org/10.1515/caim-2019-0010 | Journal eISSN: 2038-0909

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Language: English

Page range: 31 - 40

Submitted on: Nov 22, 2018

Accepted on: Dec 20, 2018

Published on: Feb 5, 2019

Published by: Italian Society for Applied and Industrial Mathemathics

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

Related subjects:

Numerical and computational mathematics,

Applied mathematics

© 2019 Clemente Cesarano, published by Italian Society for Applied and Industrial Mathemathics
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 10 (2019): Issue 1 (February 2019)