الفهرس 
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Abstract
Asmaa Moustafa Aly Soliman. New Existence Theorems for Differential
Inclusions and Some Topological Properties of the Set of Solutions. Doctor of
Philosophy Dissertation of Pure Mathematics, University Collage for Women, Ain
Shams University.
The interest in set-valued differential equations was revived in the early sixties
from the 20th century, when mathematicians become attracted to a new domain:
Control theory. Indeed many control systems can be modeled by a differential
inclusion. So, many forms of differential inclusions were investigated and theorems
of solutions for first and second order differential inclusions were studied
extensively in many papers in the literature (see e.g. [3], [13], [15], [18-22]).
The aim of this thesis is to investigate new existence theorems for different types
of differential inclusions and to study the topological properties of the set of
solutions.
This work is divided into five chapters:
In chapter one, of this thesis, we gathered definitions and some known new facts
about the properties of set-valued functions, differential inclusions and functional
differential inclusions.
In chapter two, we define the fractional Pettis and Aumann-Pettis integral for
multifunctions, we study some properties of the integrals and we study the relation
between the integrals.
In chapter three, we define the fractional Kurzweil-Henstock-Pettis and Aumann-
Kurzweil-Henstock-Pettis integral for multifunctions, we study some properties of
the integrals and we study the relation between the integrals.
In chapter four, we give an existence theorem for nonconvex semilinear functional
evolution inclusion and we study some topological properties of its solution set.
In chapter five, we give an existence theorem for semilinear functional differential
inclusion in the case when the kernel is not necessarily compact and we study some
topological properties of its solution set.
Key Words: set-valued maps, differential inclusions, functional differential
inclusions, existence theorems.