用一种新的二重积分变换求解分数阶偏微分方程

4区工程技术 Q1 Mathematics

Mathematical Problems in Engineering Pub Date : 2023-12-06 DOI:10.1155/2023/9971083

Shams A. Ahmed, Tarig M. Elzaki, Anis Mohamed

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引用次数: 0

摘要

本文利用二重Sumudu-Elzaki变换求解具有起始条件和边界条件的分数型偏微分方程。我们将使用分数阶导数(卡普托导数)的思想。对新引入的变换至关重要的定理和事实也进行了讨论和说明。利用这种新设计的积分变换及其性质，可以将fpga简化为代数方程。这个策略有精确的答案，因为它不需要任何歧视、转换或有限的假设。另外还有五个例子来支持我们的结论。结果表明，所推荐的策略是优良、可靠、高效的。它也是解决许多应用科学技术领域中具体问题的一种简单方法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Solving Partial Differential Equations of Fractional Order by Using a Novel Double Integral Transform

In this work, the double Sumudu–Elzaki transform was used for solving fractional-partial differential equations (FPDEs) with starting and boundary conditions. We will use the fractional-order derivative (Caputo’s derivatives) idea. Theorems and facts that are crucial to the newly introduced transform are also discussed and illustrated. By using this newly designed integral transform and its properties, FPDEs can be reduced into algebraic equations. This strategy has the precise answer since it does not need any discrimination, transformation, or limited assumptions. Five further instances were given to support our conclusions. The results showed that the recommended strategy is superb, reliable, and efficient. It is also a simple method for solving specific problems in a number of applied scientific and technical fields.

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来源期刊

Mathematical Problems in Engineering 工程技术-工程：综合

CiteScore

4.00

自引率

0.00%

发文量

2853

审稿时长

4.2 months

期刊介绍： Mathematical Problems in Engineering is a broad-based journal which publishes articles of interest in all engineering disciplines. Mathematical Problems in Engineering publishes results of rigorous engineering research carried out using mathematical tools. Contributions containing formulations or results related to applications are also encouraged. The primary aim of Mathematical Problems in Engineering is rapid publication and dissemination of important mathematical work which has relevance to engineering. All areas of engineering are within the scope of the journal. In particular, aerospace engineering, bioengineering, chemical engineering, computer engineering, electrical engineering, industrial engineering and manufacturing systems, and mechanical engineering are of interest. Mathematical work of interest includes, but is not limited to, ordinary and partial differential equations, stochastic processes, calculus of variations, and nonlinear analysis.