The Existence Of Solutions To Some Integro-differential Evolution Equations

The thesis is concerned with two classes of problems:the existence of solutions to the singular impulsive functional integral equations involving nonlocal conditions; the global existence of mild solutions to the semilinear fractional Cauchy problems in the α-norm. The whole thesis contains four chapters:In Chapter1we present research background of the thesis and recent developments in related problems.Chapter2considers the singular impulsive functional integral equations subject to nonlocal conditions in a Banach space. Sufficient conditions, ensuring the existence of solutions are presented.Chapter3is concerned with the local and global existence of mild solutions to a class of semilinear fractional Cauchy problems in the α-norm assuming that the operator in the linear part is the generator of a compact analytic C0-semigroup. A suitable notion of mild solution for this class of problems is also introduced.In the last Chapter, we present an application to the abstract results obtained in Chapter2.