Yalçın, Numan; Kaymak, Sinem

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.

Yalçın, Numan; Dedeturk, Mutlu

In this study, fundamental definitions and theorems of the Multiplicative Differential Transform Method (MDTM) are given. First and second order multiplicative initial value problems are numerically solved with the help of MDTM.

Yalçın, Numan

In this work, we give the power series solutions around an ordinary point, in the case of variable coefficients, homogeneous multiplicative differential equations of 2nd order. Further, we introduce the multiplicative Hermite differential equations, multiplicative Hermite polynomials and basic properties of these polynomials.

Yalçın, Numan; Çelik, Ercan

In this study, taking properties of Cauchy-Euler differential equation and Legendre differential equation, which are particular instances of linear differential equations with variable coefficients in classical analysis, as a basis, definitions of multiplicative Cauchy-Euler differential equation and multiplicative Legendre differential equation , which are types of multiplicative linear differential equations in multiplicative analysis, are given and also their solutions are investigated. In addition, multiplicative reduction of order method is given.