Solving Differential Equations Using the Modified Natural Transform

Abstract

In this manuscript, we define the modified natural transform, then we deduced the duality relationship between the Sumudu transform and the modified natural transform.

Also, we prove this relationship, and we are deducing the most important relationships and results related to the solution of differential equations.

Lastly, we conclude the most important special transform of the modified

natural transform and compared them with the transform of the Sumudu transform.

We also present applications for this relationship in ordinary and partial differential equations with constant and variable coefficients, and integral-differential equations, where using this the relationship we move to an algebraic equation directly.