الفهرس 
Chapter (1) Introduction to Fractional CalculuOnly 14 pages are availabe for public view
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Abstract
In this thesis we investigate some basics of the fractional calculus, identify some definitions of fractional integrals and fractional derivatives and reformulate some electrical and mechanical models using the generalized fractional derivatives as FODEs. Finally, we obtain the exact solutions for these FODEs using the generalized Laplace transform. The thesis is organized in four chapters as follows : In Chapter 1, we present a brief introduction to the basic concepts needed in our study. First, we introduce some basic special functions like gamma, beta, Mittag-leffler, Wright and hypergeometric functions which play an important role in fractional calculus. We define the generalized Laplace transform and its properties which help in obtaining the generalized Laplace transform of fractional integrals and fractional derivatives. Finally, we obtain the analytical solutions of some FODEs. In chapter 2, we present a brief introduction to show the benefit to describe the electrical systems using the generalized fractional operators. We develop electrical circuits using ρ-fractional derivative. Also, we obtain the analytical solutions for these electrical circuits using the properties of the ρ-Laplace transform operator. Finally, we present some numerical simulations using the obtained solutions of the electrical circuits at different values of α and ρ. In chapter 3, We study the mass-spring-damper system described by the generalized Caputo fractional derivative. We obtain the analytical solutions for mass-spring-damper system using the properties of the generalized Laplace transform operator. Finally, we present some numerical simulations using the obtained analytical solutions of the system at different values of 𝛼. In chapter 4, we give the conclusion and suggested future work.