Applications of Sumudu transform for fractional differential equations obtained with the help of proportional Caputo derivative

There are several ways to define fractional derivatives and integrals. In this thesis, the constant proportional Caputo derivative obtained as a combination of the recently emerged Caputo fractional derivative and the Riemann-Liouville integral is discussed. Thesis consists of 6 chapters. In the first two chapters, the history and importance of fractional differential equations are mentioned and necessary definitions and theorems are given. In chapter 3, the Sumudu transform and its properties are introduced and the relationships between this transform and Laplace transform are explained. In the 4th chapter, the constant proportional Caputo derivative, which has recently been added to the literature, has been extensively discussed. In the fifth chapter, some differential equations containing this derivative are solved using the Sumudu transform. In the 6th chapter, the results are mentioned.