<abstract xmlns="http://www.w3.org/1999/xhtml"><p> 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.</p></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.

Generalized special functions in the description of fractional diffusive equations

Communications in Applied and Industrial Mathematics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Starting from the heat equation, we discuss some fractional generalizations of various forms. We propose a method useful for analytic or numerical solutions....

Generalized special functions in the description of fractional diffusive equations

Published Online: Feb 05, 2019

Page range: 31 - 40

Received: Nov 22, 2018

Accepted: Dec 20, 2018

DOI: https://doi.org/10.1515/caim-2019-0010

Keywords
Hermite polynomials, heat equation, fractional calculus

© 2019 Clemente Cesarano, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Generalized special functions in the description of fractional diffusive equations

Published Online: Feb 05, 2019

Page range: 31 - 40

Received: Nov 22, 2018

Accepted: Dec 20, 2018

DOI: https://doi.org/10.1515/caim-2019-0010

KeywordsHermite polynomials, heat equation, fractional calculus

© 2019 Clemente Cesarano, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
Hermite polynomials, heat equation, fractional calculus