Hetmaniok Edyta, Pleszczyński Mariusz, Khan Yasir
Department of Mathematics Applications and Methods for Artificial Intelligence, Faculty of Applied Mathematics, Silesian University of Technology, 44-100 Gliwice, Poland.
Department of Mathematics, University of Hafr Al Batin, Hafr Al Batin 31991, Saudi Arabia.
Sensors (Basel). 2022 May 29;22(11):4124. doi: 10.3390/s22114124.
Recently, a lot of attention has been paid to the field of research connected with the wireless sensor network and industrial internet of things. The solutions found by theorists are next used in practice in such area as smart industries, smart devices, smart home, smart transportation and the like. Therefore, there is a need to look for some new techniques for solving the problems described by means of the appropriate equations, including differential equations, integral equations and integro-differential equations. The object of interests of this paper is the method dedicated for solving some integro-differential equations with a retarded (delayed) argument. The proposed procedure is based on the Taylor differential transformation which enables to transform the given integro-differential equation into a respective system of algebraic (nonlinear, very often) equations. The described method is efficient and relatively simple to use, however a high degree of generality and complexity of problems, defined by means of the discussed equations, makes impossible to obtain a general form of their solution and enforces an individual approach to each equation, which, however, does not diminish the benefits associated with its use.
最近，与无线传感器网络和工业物联网相关的研究领域受到了广泛关注。理论家们找到的解决方案随后被应用于智能产业、智能设备、智能家居、智能交通等领域。因此，有必要寻找一些新技术来解决通过适当方程（包括微分方程、积分方程和积分 - 微分方程）描述的问题。本文感兴趣的对象是一种用于求解具有滞后（延迟）自变量的积分 - 微分方程的方法。所提出的过程基于泰勒微分变换，该变换能够将给定的积分 - 微分方程转化为相应的代数（通常是非线性的）方程组。所描述的方法高效且使用相对简单，然而，通过所讨论的方程定义的问题具有高度的一般性和复杂性，使得无法获得其解的一般形式，并且需要对每个方程采用单独的方法，不过这并不减少使用该方法所带来的益处。
