Existence Results for Boundary Value Problems of Fractional Type Differential Equations

The theme of this thesis is based on the solutions of fractional differential equations. We investigate the existence and uniqueness results of the fractional differential equations with boundary value conditions. Mostly, in this thesis, one of the fractional differential equation which is the Caputo type fractional differential equation is used and also, for the boundary conditions, different types of boundary conditions are used such as nonlocal Katugampola fractional integral conditions and nonlinear boundary conditions. The existence and uniqueness results of solutions are discussed by using standard fixed point theorems such as Banach fixed point theorem, Leray-Schauder nonlinear alternative and Krasnoselskii's fixed point theorem. Furthermore, Perov's fixed point theorem is investigated for multivariable operators. Moreover, Ulam Hyers stable is studied. In addition, for the nonlinear boundary conditions of Caputo type fractional differential equation, parametrization technique is used. So, numerical analytic scheme is established for finding the successive approximations. Theories which are studied in this thesis are illustrated with examples.