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Operational method of solution of linear non-integer ordinary and partial differential equations

We propose operational method with recourse to generalized forms of orthogonal polynomials for solution of a variety of differential equations of mathematical physics. Operational definitions of generalized families of orthogonal polynomials are used in this context. Integral transforms and the oper...

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Autor principal: Zhukovsky, K. V.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2016
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4747974/
https://www.ncbi.nlm.nih.gov/pubmed/26900541
http://dx.doi.org/10.1186/s40064-016-1734-3
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author Zhukovsky, K. V.
author_facet Zhukovsky, K. V.
author_sort Zhukovsky, K. V.
collection PubMed
description We propose operational method with recourse to generalized forms of orthogonal polynomials for solution of a variety of differential equations of mathematical physics. Operational definitions of generalized families of orthogonal polynomials are used in this context. Integral transforms and the operational exponent together with some special functions are also employed in the solutions. The examples of solution of physical problems, related to such problems as the heat propagation in various models, evolutional processes, Black–Scholes-like equations etc. are demonstrated by the operational technique.
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spelling pubmed-47479742016-02-19 Operational method of solution of linear non-integer ordinary and partial differential equations Zhukovsky, K. V. Springerplus Research We propose operational method with recourse to generalized forms of orthogonal polynomials for solution of a variety of differential equations of mathematical physics. Operational definitions of generalized families of orthogonal polynomials are used in this context. Integral transforms and the operational exponent together with some special functions are also employed in the solutions. The examples of solution of physical problems, related to such problems as the heat propagation in various models, evolutional processes, Black–Scholes-like equations etc. are demonstrated by the operational technique. Springer International Publishing 2016-02-09 /pmc/articles/PMC4747974/ /pubmed/26900541 http://dx.doi.org/10.1186/s40064-016-1734-3 Text en © Zhukovsky. 2016 Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Research
Zhukovsky, K. V.
Operational method of solution of linear non-integer ordinary and partial differential equations
title Operational method of solution of linear non-integer ordinary and partial differential equations
title_full Operational method of solution of linear non-integer ordinary and partial differential equations
title_fullStr Operational method of solution of linear non-integer ordinary and partial differential equations
title_full_unstemmed Operational method of solution of linear non-integer ordinary and partial differential equations
title_short Operational method of solution of linear non-integer ordinary and partial differential equations
title_sort operational method of solution of linear non-integer ordinary and partial differential equations
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4747974/
https://www.ncbi.nlm.nih.gov/pubmed/26900541
http://dx.doi.org/10.1186/s40064-016-1734-3
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