الفهرس 
صفحة العنوان باللغة الانجليزيةOnly 14 pages are availabe for public view
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Abstract
Summary
It is known that the time delay in systems is associated with a change of
time to achieve the target of the system. For this reason we interested in
finding the solution of some models with the delay of the differential equation
and for accuracy and precision solution of models with the delay in a
fractional differential equation.
This thesis consists of five chapters and a reference list at the end of the thesis.
The thesis is organized as follows:
Chapter one
This chapter contains, the basic definitions, some properties concerning the
existence and the uniqueness of the solutions of fractional differential equations
and introduction to delay differential equations. Also, it contains some
applied mathematical models. Moreover, it contains the aim and objectives
of this thesis.
Chapter two
This chapter is introductory and comprises of historical background, recent
developments, a literature survey on the subject and allied fields in addition
to the outline of basic governing equations of the fractional differential equations.
III
Chapter three
Delay differential equations have several features which make their analysis
more complicated. This chapter is concerned with studying the delay differential
equations, and their types, and some application.
Chapter four
The increasing interest in applications of delay differential equation has motivated
the development and the investigation of an exact and numerical method
specifically devised to solve delay differential equations of fractional
order. So we studied the analytical method to solve delay differential equations
of fractional order. We took their models to solve their analytically;
the space-time fractional potential Kadomstev – Petviashvili (PKP) equation
with delay, Burgers’ equation with delay, Allen-Cahn equation with delay,
and the space-time fractional modified Benjamin–Bona–Mahony (MBBM)
equation with delay.
Chapter five
In