A New Integral Transform “The Modified Natural Transform”, Its Properties and Applications

Abstract

In this manuscript, we propose a new integral transform called the Modified Natural Transform. This transform can be considered as a base for several potential new integral transforms. Many fundamental properties about this new integral transform were created in this work. These properties include, for

example, the existence theorem, the Modified Natural Transform of Derivatives theorem, convolution theorem, and inverse Modified Natural Transform. The main advantage of this new technique is its ability to solve differential equations with variable and constant coefficients. To demonstrate the efficiency and utility of the presented transform for solving differential equations,         several examples are provided.