NEW INTEGRAL OPERATOR FOR SOLUTIONS OF DIFFERENTIAL EQUATIONS

*ALI OZYAPICI, TOLGAY KARANFILLER (pp. 131-143)*#### Abstract

This study is aimed to define general representation of integral transforms for solving differential equations. The Generalized Integral Transform consists of the well-known Laplace transform, Sumudu transform, Tarig transform and Elzaki transform, as a common coverage. Since all these transforms, respectively, promise an effective usage for solving differential equations, their corresponding theories can easily be derived by using Generalized Integral Transform. Moreover, this study shows that Generalized Integral Transform can be easily used to define a new integral operator which will provide the easiest approach to solution of the given differential equation. Some examples discussed in the paper show that the Generalized Integral Transform can be applicable for many differential equations while Laplace transform can not be applicable for the same differential equations.

#### Keywords

integral transform , Sumudu transform, Elzaki transform, Laplace transform.