Solving non-homogeneous non-Linear difference and differential equations by using additive and multiplicative derivative and integral with applications

Difference equations are discrete analogy of the differential equations. These equations appearin mathematical modeling of physics and engineering problems, economic and population subjects thatdeal with discrete data and variables.In this article, we consider and solve these types of equations that are non-homogeneous and non-linear.The solving method is performed using by multiplicative discrete and continuous differential equations.The importance of this method is that by using the concept of discrete derivative, the analytical methodand analytical solutions are given to linear and non -linear non-Homogeneous difference and differentialequations.

Keywords:

Invariant Functions , Non- Linear Difference Equations , Non-Homogenuous difference equation , Discrete additive derivative , Discrete multiplicative derivative