Discussion of Ph.D. Dissertation  in the College of Computer Science and Mathematics – Department of Mathematics Sciences entitled:

“ Approximate and Intelligent Techniques for Solving Partial Integral- Differential Equations “

It was discussed in the discussion room at the Faculty of Computer Science and Mathematics at the University of Mosul on Thursday, 14 -5-2026.

Ph.D. Dissertation by Student Hiba Shuker mahmmod Ahmad

under the supervision of Prof. Dr. Ahmed  Farooq Qasim

Partial integro-differential equations (PIDEs) are a class of equations that combine partial differentiation and integration of an unknown function. This type of equation plays a significant role in many fields of science and engineering. They arise in the modeling of complex physical and biological phenomena, such as heat transfer, chemical reactions, thermoelasticity, diffusion, and nuclear reactor dynamics.

There are numerous analytical and approximate methods for solving PIDEs. Among them, the Banach Contraction Method (BCM) and the Residual Power Series Method (RPSM) have been employed. Numerical results have demonstrated the efficiency of these methods in solving such equations. Moreover, both methods have been generalized to handle equations of higher orders and more complex structures, along with the development of theorems that guarantee the stability and convergence of the approximate solutions.

In the context of the growing interest in artificial intelligence, an alternative approach based on machine learning algorithms has been introduced. In this approach, a feedforward neural network is trained to learn the solutions of equations directly from data, opening new horizons for handling high-dimensional problems.

Furthermore, the BCM has been applied to study and analyze an age-structured SIR epidemic model. This application aims to evaluate the impact of dynamic control policies, such as age-targeted vaccination, on the spread of the disease, highlighting the practical importance of the developed mathematical methods in addressing pressing real-world problems.

The scientific committee included the following members:

• Dr. Abdulghafor Mohammed Ameen Khudhur – Chairman
• Dr. Waleed Mohammed Fathi – Member.
• Dr. Muhannad Ahmed Mahmud – Member.
• Prof. Dr.Ahmed Entesar Githeeth – Member.
• Prof. Dr. Mohammed Omar Shaaban- Member.
• Dr. Ahmed Farooq Qasim – Member and supervisor.