A new approach to fractional differential equations

IF 1.1 4区工程技术 Q4 THERMODYNAMICS Thermal Science Pub Date : 2023-01-01 DOI:10.2298/tsci23s1301a

Hussam Alrabaiah, S. Hussain, Sami Awan, A. Zeb, K. Shah, T. Abdeljawad

引用次数: 0

Abstract

In this work, we define fractional derivative of order ? > 0, with no restrictions on the domain of the function, and give its geometry. We derive some rules and properties for the proposed new approach and show that if fractional order converges to an integer order, then each rule converges to the corresponding rule of derivative under this integer. On applications side we show that it has ability to convert various type of FDE to ODE and vice versa. Finally, we solve several FDE given in literature through the new approach.

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分数阶微分方程的一种新方法

在这项工作中，我们定义了阶导数的分数?> 0，对函数的定义域没有限制，并给出它的几何形状。我们推导了该方法的一些规则和性质，并证明了分数阶收敛于整数阶，则每条规则收敛于该整数下相应的导数规则。在应用程序方面，我们展示了它能够将各种类型的FDE转换为ODE，反之亦然。最后，我们用新方法求解了文献中给出的几个FDE。

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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来源期刊

Thermal Science 工程技术-热力学

CiteScore

2.70

自引率

29.40%

发文量

399

审稿时长

5 months

期刊介绍： The main aims of Thermal Science to publish papers giving results of the fundamental and applied research in different, but closely connected fields: fluid mechanics (mainly turbulent flows), heat transfer, mass transfer, combustion and chemical processes in single, and specifically in multi-phase and multi-component flows in high-temperature chemically reacting flows processes present in thermal engineering, energy generating or consuming equipment, process and chemical engineering equipment and devices, ecological engineering, The important characteristic of the journal is the orientation to the fundamental results of the investigations of different physical and chemical processes, always jointly present in real conditions, and their mutual influence. To publish papers written by experts from different fields: mechanical engineering, chemical engineering, fluid dynamics, thermodynamics and related fields. To inform international scientific community about the recent, and most prominent fundamental results achieved in the South-East European region, and particularly in Serbia, and - vice versa - to inform the scientific community from South-East European Region about recent fundamental and applied scientific achievements in developed countries, serving as a basis for technology development. To achieve international standards of the published papers, by the engagement of experts from different countries in the International Advisory board.