Analysis of fractional differential equations with integral transforms

The thesis is organized in nine chapters. In the first chapter, general information about fractional differential equations and integral transforms is given. In the second chapter, basic definitions and theorems are given. In the third chapter, Gamma function, Beta function and Mittag-Leffler function, which are special functions are introduced. In the fourth chapter, different transforms such as Laplace, Sumudu, Elzaki, Natural, Aboodh, α-İntegral Laplace, Pourreza, Mohand, Sawi, Kamal and G-transform are introduced and the basic properties of these transforms are given. In the fifth chapter, fractional derivatives and integrals, Riemann-Liouville fractional derivative, Caputo fractional derivative and Atangana-Baleanu fractional derivative in the sense of Caputo are introduced. In the sixth chapter, integral transforms and applications of Caputo fractional derivative are given. In the seventh chapter, integral transforms and applications of Mittag-Leffler function are given. In the eighth chapter, integral transforms and applications of Atangana-Baleanu fractional derivative in terms of Caputo are given. In the ninth chapter, the results are given.