Approximation methods of Fractional Derivatives and Their Applications to Fractional Differential Equations
Date
2017-08-02
Authors
ظاهر, أصيل فازع حمد
Journal Title
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Publisher
جامعة النجاح الوطنية
Abstract
Fractional calculus is a field of mathematics which concern on finding derivatives or integrals of non-integer order. The exact birthday of fractional calculus was in september 30, 1695.
Over the years, many mathematicians contributed to this field, and bit by bit the importance of fractional calculus has appeared in many aspects of our life, such as physics, engineering, viscoelasticity, and many others.
In this thesis, we start our work in chapter 1 by focusing on the definition of Riemann-Liouville fractional integral, and finding the fractional integral of any order p for many functions.
In chapter 2, we study the two mostly used definitions of fractional differentiation namely; the Riemann-Liouville and the Caputo definitions, then we make comparison between the two definitions of fractional derivatives. In chapter 3, we focus on solving fractional initial value problems with Caputo operator or with Riemann-Liouville operator using the easiest method which is Laplace transform method.
At the end of this thesis, we focus on some applications of fractional calculus in real life such as tautochrone problem.