Nonlinear Sequential and Non Sequential Fractional Differential Equations with Integral Boundary Conditions

This thesis relies on various fractional differential equations. Based on the classical fixed point theorem summarized by what known as the Banach contraction mapping theorem, nonlinear alternative of Leray-Schauder type and Krasnoselskii’s fixed point theorem, a three different nonlinear fractional differential equations are considered. In chapter four we study the existence and uniqueness for the solution of the nonlinear sequential fractional differential equation involving Caputo fractional derivative and associated with nonlocal integral boundary conditions. In chapter five with a little modifications on the same problem mentioned in the previous chapter lead us to define a new function space with different norm, the boundary condition for this problem can be considered as a generalization of the boundary conditions associated with the problem in chapter four. For these two chapters we illustrate our results by examples given at the end of each one. Whereas, in chapter six which can be considered as two parts, we investigate the existence and uniqueness for the solution of the nonlinear fractional differential equations involving Hadamard and Caputo-Hadamard fractional derivative associated with three points integral boundary conditions, for the applicability of our results we give some examples at the end of this chapter as well. Keywords: fractional differential equation, sequential, Caputo, Hadamard, nonlocal integral boundary conditions