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 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.
