Qualitative Theory of Fractional Differential Equations

Abstract

Main focus of interest of this study is to establish the existence and stability theory for various classes of ordinary and partial fractional differential equations. This dissertation starts with the introduction to some basic concepts, notations and definitions from fractional calculus and fixed point theory. Existence of solution, stability results and oscillation criteria are developed for initial value problems. Sufficient conditions for the existence of positive solutions and multiple positive solutions to generalized fractional differential equations with p-Laplacian and ð€€€fractional differential equations with two point and three point boundary conditions are established. Furthermore, measure of noncompactness is used to develop existence of solution of an infinite system of generalized fractional differential equation. Inequalities and global existence results are given for a terminal value problem. Moreover, we discuss a fractional version of Duhamel’s principle for a class of fractional partial differential equations. And lastly, existence results are built up for generalized impulsive fractional partial differential equations.