We present a new general complex integral transform in this study. This complex transform properties are studied. The main problem is reduced to a simple algebraic equation using this complex integral transformation. By solving this algebraic equation and using the inverse of the general complex integral transform, the answer to this main problem can be found. Finally, the solution to linear higher order ordinary differential equation is found by using the new general complex integral transform. We also present and discuss a number of key real-life problems, such as pharmacokinetics and nuclear physics.

Many integral transformations have been proposed, tasted and proven to solve many applications in various scientific fields. The diversity of integral transformations comes from their unique ability to solve problems by transforming them from one domain where the solution is given by a complex mathematical procedure to another domain where simple algebraic methods can solve them. On this basis, many of these transformations and knowledge appeared on the field of real numbers and the field of complex numbers. The reason for the diversity of these transforms is the need for them in solving some mathematical equations and physical equations or that pertain to any branch of applied sciences, so they have proven their strength in solving differential and complementary equations and differential systems in addition to scientific applications. The Laplace Transform was one of the first transformations that contributed to the solution of mathematical equations, and then dozens of transformations appeared, which depended mainly on the Laplace Transform. This work demonstrates the temporal diversity of the integral transformations by presenting a group of integral transformations with their basic characteristics. We dealt with single and double integrals

The Population growth and decay issues are one of the most pressing issues in many sectors of study. These issues can be found in physics, chemistry, social science, biology, and zoology, among other subjects. We introduced the solution for these problems in this paper by using the SEJI (Sadiq- Emad- Jinan) integral transform, which has some mathematical properties that we use in our solutions. We also presented the SEJI transform for some functions, followed by the inverse of the SEJI integral transform for these functions. After that, we demonstrate how to use the SEJI transform to tackle population growth and decay problems by presenting two applications that demonstrate how to use this transform to obtain solutions. Finally, we conclude that the SEJI transform can readily solve the problems of population increase and decay, and that the action of this integral transform in overcoming these challenges can be explained through applications.

In this paper, a novel concept for a double transform in two dimensions known as the double SEJI integral transform has been proposed. Its key characteristics, including a few of its properties and theorems, have been established. A few well-known functions were also available in the Double SEJI integral transform. Later, we learn about brand-new research on partial fractional Caputo derivatives and partial differential derivatives. Finally, we apply this new transform to various first- and second-order partial differential equations.