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Abstract
In this paper, differential transformation method is used to find exact solutions of nonlinear delay integro– differential equations. Many theorems are presented that required for applying differential transformation method for nonlinear delay integro–differential equation. The validity and efficiency of the proposed method are demonstrated through several tests.
Highlights
Finding the analytical solutions of functional equations has been devoted attention of mathematicians's interest in recent years
! = {(, ): − ̃ ≤ ≤, ∈ }, Here $ ∈ (0,1), for ' = 0,1, are the coefficients of vanishing delay function (( ) = $, which is used in the pantograph equation, and $ > 0, for ' = 0,1, are the constants of non-vanishing delay (( ) = − $, that is a classical case of delay functions
There exist few numerical techniques applied to solving delay integro– differential equation
Summary
Finding the analytical solutions of functional equations has been devoted attention of mathematicians's interest in recent years. Delay integro–differential equations are usually difficult to solve analytically so it is required to obtain an efficient approximate solution. They have been of great interest by several authors. The given differential equation and related initial conditions are transformed into a recurrence equation that leads to the solution of a system of algebraic equations as coefficients of a power series solution This method is useful for obtaining exact and approximate solutions of linear and nonlinear differential equations. We will extend one–dimensional differential transformation method (DTM), by presenting and proving some new theorems, to solve a class of nonlinear delay integro– differential equation which it's kernel function is involve delay (vanishing and non–vanishing delays).
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