نوع المشرف

مشرف رئيسي

تاريخ الاشراف على الرسالة من

2015

الى

2015

اسم الطالب

زايد الزهيري

ملخص الرسالة

ractional calculus is a generalization of ordinary (integer order) differentiation and integration to its fractional (non-integer) order. Almost every problem in calculus can be revisited at a whole new level ,with much more flexibility in solving real-life problems in applied sciences, engineering, economics, control theory , communication systems and many other fields. Numerous problems in many applications are modeled mathematically by fractional differential equations (systems) such as dynamical system, chaotic system , star network of coupled systems and population of star coupled oscillators. In this work, we study the two most definitions of fractional calculus commonly used. they are Riemann-Liouville and Caputo fractional operators and collect a list of rules and properties related to these operators. Furthermore, some fractional differential equations in Caputo sense are also studied and solved by using Laplace Method. Finally, we present the general solutions of some non-homogeneous (matrix) fractional-order systems by using the Kronecker (Hadamard) products and vector (diagonal extraction) operators methods with some illustrative examples.