الفهرس | Only 14 pages are availabe for public view |
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 |