Master’s Thesis Defense at the College of Computer Science and Mathematics/ Department of Mathematics Sciences entitled:

“Solution of an Integral-Differential Equations Using Integral Transform Methods”

the Master’s thesis of the student Hedra Abreem Yalda Khaee was discussed on

Monday, 7/7, 2025, in the discussion hall at the College of Computer Science and Mathematics, University of Mosul, under the supervision of Prof. Dr. Abdulgafour Mohammed Amin.

In this thesis, we focus on the application of integral transform methods to solve linear and nonlinear integro-differential equations. We apply the combined Kashuri & Fundo transform with the Adomian decomposition method to obtain the approximate solution for one-dimensional nonlinear Volterra integro-differential equations. We also use the Kashuri & Fundo transform, Natural transform, and Jafari transform methods of two-dimensional function to solve two-dimensional linear partial integro-differential equations. Additionally, we combine the Jafari transform and Natural transform methods of two-dimensional function with the Adomian decomposition method to approximate the solution for two-dimensional nonlinear partial integro-differential equations. The effectiveness of these methods is demonstrated through several test cases, which highlight their ability to simplify the solution process and enhance computational efficiency.

The Examination Committee included:

Prof. Dr. Ekhlas Saadallah Ahmed/ Committee Chair

Asst. Prof. Dr. Ahmed Farooq Qasim/ Committee Member

Asst. Prof. Dr. Suzan Hassan Mohammad/ Committee Member

Prof. Dr. Abdulghafor Muhammad Amin/ Committee Member (Supervisor)