Solving fractional partial differential equations via a new scheme

Ahmad Qazza; Rania Saadeh; Emad Salah; Ahmad Qazza; Rania Saadeh; Emad Salah

doi:10.3934/math.2023267

AIMS Mathematics

2023, Volume 8, Issue 3: 5318-5337. doi: 10.3934/math.2023267

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Research article

Solving fractional partial differential equations via a new scheme

Department of Mathematics, Faculty of Science, Zarqa University, Zarqa 13110, Jordan

Received: 16 September 2022 Revised: 30 October 2022 Accepted: 17 November 2022 Published: 14 December 2022
MSC : 35R11, 40G10

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.
- fractional differential equations,
- time fractional partial differential equations,
- analytical solution,
- power series
Citation: Ahmad Qazza, Rania Saadeh, Emad Salah. Solving fractional partial differential equations via a new scheme[J]. AIMS Mathematics, 2023, 8(3): 5318-5337. doi: 10.3934/math.2023267

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Abstract

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.

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