On Bigeometric Laplace Integral Transform

Year 2023, Volume: 13 Issue: 3, 2042 - 2056, 01.09.2023

Sinem Kaymak Numan Yalçın

https://doi.org/10.21597/jist.1283580

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.

Keywords

Bigeometric analysis, Exponential arithmetic, Bigeometric derivative, Bigeometric integral, Bigeometric Laplace integral transform

Bigeometric Laplace İntegral Dönüşümü Üzerine

Abstract

Bu çalışmanın amacı, klasik analizin integral dönüşüm metotlarından biri olan Laplace integral dönüşümünün temel tanım ve teoremleri kullanılarak, Newtonyen olmayan analizlerden biri olan bigeometrik analizde Laplace integral dönüşümünü tanımlamaktır. Öncelikli olarak Newtonyen olmayan analizlerin temelini oluşturan üstel aritmetik kavramı verilmiştir. Klasik
analizde olduğu gibi bigeometrik analizde de bigeometrik limit, bigeometrik süreklilik, bigeometrik türev ve bigeometrik integral kavramlarının tanımları verilmiştir. Ardından,
bigeometrik Laplace integral dönüşümünün tanımı yapılmıştır. Sonra, bigeometrik Laplace integral dönüşümünün bazı temel kavramları ve teoremleri verilmiştir. Bunun için bigeometrik
analizde yer alan bigeometrik türev, bigeometrik belirsiz integral ve bigeometrik belirli integral kavramlarının tanımları ve bu kavramların özellikleri kullanılmıştır. Ayrıca, bigeometrik
Laplace integral dönüşümünün özellikleri incelenmiştir. Son olarak bigeometrik Laplace integral dönüşümü yardımıyla bigeometrik lineer diferansiyel denklemlerin çözümleri araştırılmıştır.

Keywords

Bigeometrik analiz, Üstel aritmetik, Bigeometrik türev, Bigeometrik integral, Bigeometrik Laplace integral dönüşümü

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