دراسة وتطوير بعض خواص تحويل Iman لحل المعادلات التفاضلية العادية وبعض التطبيقات العملية

Abstract

In this paper, we present the Iman transform as a new and improved integral transformation of the Laplace and Sumudu transforms for solving differential equations with coefficients that som traditional transformations, such as the sumudu transform, could not solve. In this work, the theoretical properties of the Iman transform were developed through a number of theorems and proofs. The Iman transform was also used to solve typical problems such as population growth models and radioactive decay models. The result demonstrated the effectiveness of Iman transform in finding exact solutions while reducing the number of calculations compared to traditional methods. The study also demonstrated the match between the solutions of the Iman transform and the solutions of the Laplace transform in some special cases, confirming the accuracy and efficiency of this transformation.