# Exact Solution of System of Multi-Photograph Type Delay Differential Equations Via New Algorithm Based on Homotopy Perturbation Method

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## Keywords:

HPM Procedure, Series Expansion, Laplace Trans-form, Pade Approximant, Pantograph equations## Abstract

A new algorithm is proposed in this paper to explain how the modified homotopy perturbation approach can be successfully implemented based on the Pade approximants and the Laplace transformin order to acquire the accurate solutions of a nonlinear system of multiphotographdelay differential equations. The method that has been suggestedhas the benefit of giving exact solutions, and it is simple to implementanalytically on the issues that have been presented. Examples have been provided to demonstrate that this strategy may be utilized andis successful in its application. The results show that the method thatwas described could be used to solve many different types of differential equations.

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