Solution of Fractional Partial Differential Equations Using Fractional Power Series Method

In this paper, we are presenting our work where the noninteger order partial differential equation is studied analytically and numerically using the noninteger power series technique, proposed to solve a noninteger differential equation. We are familiar with a coupled system of the nonlinear partial...

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Autores principales:	Asif Iqbal Ali, Muhammad Kalim, Adnan Khan
Formato:	article
Lenguaje:	EN
Publicado:	Hindawi Limited 2021
Materias:	Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/2f0c5529e64d490388e44c7e8fac3f34
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spelling	oai:doaj.org-article:2f0c5529e64d490388e44c7e8fac3f342021-11-15T01:19:33ZSolution of Fractional Partial Differential Equations Using Fractional Power Series Method1687-965110.1155/2021/6385799https://doaj.org/article/2f0c5529e64d490388e44c7e8fac3f342021-01-01T00:00:00Zhttp://dx.doi.org/10.1155/2021/6385799https://doaj.org/toc/1687-9651In this paper, we are presenting our work where the noninteger order partial differential equation is studied analytically and numerically using the noninteger power series technique, proposed to solve a noninteger differential equation. We are familiar with a coupled system of the nonlinear partial differential equation (NLPDE). Noninteger derivatives are considered in the Caputo operator. The fractional-order power series technique for finding the nonlinear fractional-order partial differential equation is found to be relatively simple in implementation with an application of the direct power series method. We obtained the solution of nonlinear dispersive equations which are used in electromagnetic and optics signal transformation. The proposed approach of using the noninteger power series technique appears to have a good chance of lowering the computational cost of solving such problems significantly. How to paradigm an initial representation plays an important role in the subsequent process, and a few examples are provided to clarify the initial solution collection.Asif Iqbal AliMuhammad KalimAdnan KhanHindawi LimitedarticleMathematicsQA1-939ENInternational Journal of Differential Equations, Vol 2021 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Mathematics QA1-939
spellingShingle	Mathematics QA1-939 Asif Iqbal Ali Muhammad Kalim Adnan Khan Solution of Fractional Partial Differential Equations Using Fractional Power Series Method
description	In this paper, we are presenting our work where the noninteger order partial differential equation is studied analytically and numerically using the noninteger power series technique, proposed to solve a noninteger differential equation. We are familiar with a coupled system of the nonlinear partial differential equation (NLPDE). Noninteger derivatives are considered in the Caputo operator. The fractional-order power series technique for finding the nonlinear fractional-order partial differential equation is found to be relatively simple in implementation with an application of the direct power series method. We obtained the solution of nonlinear dispersive equations which are used in electromagnetic and optics signal transformation. The proposed approach of using the noninteger power series technique appears to have a good chance of lowering the computational cost of solving such problems significantly. How to paradigm an initial representation plays an important role in the subsequent process, and a few examples are provided to clarify the initial solution collection.
format	article
author	Asif Iqbal Ali Muhammad Kalim Adnan Khan
author_facet	Asif Iqbal Ali Muhammad Kalim Adnan Khan
author_sort	Asif Iqbal Ali
title	Solution of Fractional Partial Differential Equations Using Fractional Power Series Method
title_short	Solution of Fractional Partial Differential Equations Using Fractional Power Series Method
title_full	Solution of Fractional Partial Differential Equations Using Fractional Power Series Method
title_fullStr	Solution of Fractional Partial Differential Equations Using Fractional Power Series Method
title_full_unstemmed	Solution of Fractional Partial Differential Equations Using Fractional Power Series Method
title_sort	solution of fractional partial differential equations using fractional power series method
publisher	Hindawi Limited
publishDate	2021
url	https://doaj.org/article/2f0c5529e64d490388e44c7e8fac3f34
work_keys_str_mv	AT asifiqbalali solutionoffractionalpartialdifferentialequationsusingfractionalpowerseriesmethod AT muhammadkalim solutionoffractionalpartialdifferentialequationsusingfractionalpowerseriesmethod AT adnankhan solutionoffractionalpartialdifferentialequationsusingfractionalpowerseriesmethod
_version_	1718428913932173312

Solution of Fractional Partial Differential Equations Using Fractional Power Series Method

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