Series solutions of the fractional differential equations

This thesis consists of seven main chapters. In the first chapter, the development of fractional analysis is mentioned and information is given about the methods applied to fractional differential equations in the literature. In the second chapter, some special functions are given. In the third chapter, fractional derivative and fractional integrals are given for solutions of fractional differential equations. In the fourth chapter, the residual power series method is defined and the residual power series method is applied to fractional partial differential equations and systems of equations. In the fifth chapter, restricted fractional differential transformation method is given and applied to fractional differential equations. In the sixth chapter, Adomian decomposition method is given, applied to nonlinear fractional differential equations and approximate solutions are obtained. At the same time, serial solutions of the conformable fractional nonlinear Lane-Emden differential equation in terms of Adomian polynomials are obtained. In the seventh chapter, the series solution method suitable for the Taylor series expansion is given for the nonlinear fractional differential equation.