College of Education for Pure Science

Master Thesis Viva in the College of Education for Pure Science entitled ” Numerical Solution for Solving Fractional Differential Equations Using Chebyshev Wavelets”

The College of Education for Pure Science, University of Mosul, has done the Master Thesis Viva entitled ” Numerical Solution for Solving Fractional Differential Equations Using Chebyshev Wavelets “,

On Sunday, September 10 2023, the College staff including the respected Dean of the College, Assistant Professor Dr. Qais Ismail Ibrahim, the Honorable Scientific Associate and Administrative Associate, the Honorable Head of the Department of Mathematics, and a number of the college’s teachers were attended the viva.

In this study, presented by the Master student Inaam Abdulbaset Fathi in the Department of Mathematics, a numerical method was proposed to solve fractional (ordinary and partial) differential equations using Chebyshev wavelets. Two algorithms were presented, the first for solving fractional ordinary differential equations and the second for solving fractional partial differential equations. In the first algorithm, Chebyshev matrix and Chebyshev operational matrix were used for fractional integration. In the second algorithm, in addition to these two matrices, a transposed Chebyshev matrix was used. These matrices are used to transform differential equations into algebraic equations. The Chebyshev matrix is obtained from the Chebyshev wavelet, which relies on Chebyshev polynomials. The Chebyshev operational matrix for fractional integration is obtained from the pulse mass function matrix with the Chebyshev matrix.

Several examples were provided to demonstrate the effectiveness and applicability of the algorithms. The approximate solution obtained from applying the algorithms was compared with the exact solution, and the absolute error and root mean square error were calculated. The results showed a close agreement with a small error rate.

The Viva committee was chaired by Prof. Dr. Saad Shakir Mahmood / College of Education, Mustansiriya University and the membership of Asst. Prof. Dr. Abdel Ghafoor Mohamedamine Khadr / College of Computer Science and Mathematics /University of Mosul, Asst. Prof. Dr. Maha Salah Younes / College of Education for Pure Science /University of Mosul and under the supervision and membership of Asst. Prof. Dr. Kais Ismail Ibraheem / The respected Dean of the College of Education for Pure Science /University of Mosul.