College of Computer Science and Mathematics

Discussion of a Doctorial Dissertation in the College of Computer Science and Mathematics – Department of Mathematics Sciences entitled:”Investigation of Numerical and Analytical Methods for Solving Fractional Partial Differential Equations”In continuation of the scientific research movement and with the follow-up and presence of the Dean of the College of Computer Science and MathematicsProf. Dr. Duha Bashir Abdullah The esteemedIt was discussed in the discussion room at the Faculty of Computer Science and Mathematics at the University of Mosul on Thursday23-2-2023Doctorial Dissertation by student Mohammed Omar Shaaban Al-Amr, under the supervision ofAssist. Prof. Dr.Abdulghafor M. Al-RozbayaniThe present study is devoted to study the analytical and numerical solutions of the spatio-temporal fractional (1+1)-dimensional and (2+1)-dimensional double-stranded DNA equations with a novel fractional derivative operator, namely the beta fractional derivative. Three effective prolific methods are used to construct analytical and numerical solutions of the models under consideration. These methods are the exp(-Ψ(η)) expansion, the extended Bernoulli sub-ODE, and the differential transform methods. Various types of traveling wave structures of biological relevance are successfully constructed. The approximate solutions are found in the form of finite series. It is demonstrated that the employed approaches are highly effective and robust for a broad range of FPDEs in real-world problems.The scientific committee included the following members:

• Rostam K. Saeed- Chairman
• Ekhlass S. Ahmed- Member
• Thair Y. Thanoon – Member
• Kais I. Ibraheem – Member
• Waleed M. Al-Hayani – Member
• Abdulghafor M. Al-Rozbayani – Member and Supervisor