Fıxed Point Approach To Fractional Order Differantial Equations

In this thesis, existence and uniqueness conditions for initial value problems involving fractional integrals were investigated. Also, a fixed point approach was used to solve these initial value problems. In the first chapter, some information was given about the historical development and importance of the subject with the literature review. In the second chapter, some basic definitions, theorems and examples that will be used in the thesis were expressed. In the third chapter, information about solution methods for fractional differential equations was given and power series method and Laplace transform method were explained with examples. In the last chapter, existence and uniqueness conditions of initial value problems containing some fractional integro-differential equations were investigated. The results were supported with examples.