Solving fractional partial differential equations via a new scheme

In this paper, we introduce a new technique, called the direct power series method to solve several types of time-fractional partial differential equations and systems, in terms of the Caputo derivative. We illustrate the method with a simple algorithm that can be used to solve different types of ti...

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Bibliographic Details
Published inAIMS mathematics Vol. 8; no. 3; pp. 5318 - 5337
Main Authors Qazza, Ahmad, Saadeh, Rania, Salah, Emad
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2023
Subjects
analytical solution
fractional differential equations
power series
time fractional partial differential equations
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ISSN2473-6988
2473-6988
DOI10.3934/math.2023267

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Summary:In this paper, we introduce a new technique, called the direct power series method to solve several types of time-fractional partial differential equations and systems, in terms of the Caputo derivative. We illustrate the method with a simple algorithm that can be used to solve different types of time-fractional partial problems. We introduce a new theorem to explain the required substitutions of the proposed method. In addition, convergence analysis conditions of the method are given. Furthermore, some different illustrative examples of time-fractional partial differential equations and systems are discussed to show the applicability and simplicity of the new approach.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2023267