Numerical treatment of certain fractional and non-fractional differential equations

Abstract

I wish to express my greatest thanks for all people who help me, encourage me and company with me during all the Ph.D. time.First of all, I wish to express my sincere gratitude to my supervisor, Wong Jia Yiing, Patricia. She is very professional in the fields including computational mathematics, di↵erential equations and spline analysis. With her patient guidance, I can obtain a newer and deeper understanding of mathematics. Meanwhile, I learned how to write a scientific paper through her instructions. She also provided good research communication chances for me like participating oversea conferences. Besides the help in academic, she taught me how to face the di culties in life and kept encouraging me to overcome them.Next, I wish to express my honest thanks to my parents, who always gives their inexhaustible love to me. They gave me the chance that I can complete my Ph.D.in Singapore. They had to overcome some di culties by themselves, as I can't company with them. They are industrious and brave. I would try my best to return their love.Last but not least, I wish to express my love to my girlfriend, Shan Ye, who brings the happiness to me. I also want to express my thanks to my dear friends Zhenghua