On Bigeometric Laplace Integral Transform

Numan Yalçin, Sinem Kaymak
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Abstract

The purpose of this study is to mention the Laplace integral transform in bigeometric analysis, which is one of the non-Newtonian analysis by using the fundamental definitions and theorems of the Laplace integral transform, which is one of the integral transform methods of classical analysis. First of all, the concept of exponential arithmetic, which forms the basis of non Newtonian analysis, is given. As in classical analysis, definitions of the concepts of bigeometric limit, bigeometric continuity, bigeometric derivative and bigeometric integral are given in bigeometric analysis. Here, the definition of the bigeometric Laplace integral transform in bigeometric analysis is given. Then, some basic concepts and theorems of the bigeometric Laplace integral transform are given. For this purpose, the definitions of the concepts of bigeometric derivative and bigeometric indefinite integral and bigeometric definite integral in bigeometric analysis and the properties of these concepts are used. In addition, the properties of the bigeometric Laplace integral transform are investigated. Finally, solutions of bigeometric linear differential equations are investigated with the help of the bigeometric Laplace integral transform.
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关于大几何拉普拉斯积分变换
本研究的目的是利用经典分析中的积分变换方法之一——拉普拉斯积分变换的基本定义和定理,提一提非牛顿分析中的非几何分析中的拉普拉斯积分变换。首先,给出了指数算法的概念,它是非牛顿分析的基础。与经典分析一样,在几何分析中给出了几何极限、几何连续、几何导数和几何积分等概念的定义。本文给出了大几何拉普拉斯积分变换在大几何分析中的定义。然后给出了大几何拉普拉斯积分变换的一些基本概念和定理。为此,使用了几何分析中几何导数、几何不定积分、几何定积分等概念的定义以及这些概念的性质。此外,还研究了大几何拉普拉斯积分变换的性质。最后,利用大几何拉普拉斯积分变换研究了大几何线性微分方程的解。
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