الفهرس 
Chapter 1 IntroductionOnly 14 pages are availabe for public view
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Abstract
The main purpose of the thesis is to study qualitative behavior of some nonautonomous nonlinear fractional order differential equations and use the chaotic time series generated from the nonautonomous nonlinear systems in image encryption. This thesis is organized as follows: In chapter one, an overview of fractional calculus, fractional dynamical systems, some definitions and theorems used for stability analysis are presented. In addition, an overview of using chaotic fractional systems in image encryption, thesis outline and work objectives are introduced. In chapter two, a novel fractional nonautonomous system is proposed in the form of fractional order meminductor-memristor based circuit. Four circuit models are presented by different arrangements of the elements and the dynamic behaviors for each circuit are explored. It is observed that the four systems exhibit chaotic and hyperchaotic behaviors which have been verified using Lyapunov exponents. Bifurcation diagrams and phase portraits are employed to examine the effects of parameters variation on the qualitative dynamics of each model. An image encryption scheme is presented based on pseudo chaos orbit generated by two interval extensions of chaotic circuit model. The security analysis is carried out to verify the robustness and the efficiency of the encryption scheme against possible attacks. In chapter three, the occurrence of ghost attractor is verified in three cases of a proposed fractional order R¨ossler blinking system. Firstly, the dynamical behaviors of fractional order prototype-4 R¨ossler system with Chua’s diode are explored via stability analysis, bifurcation diagrams and Lyapunov exponents. It is depicted that this system exhibits a variety of dynamics including like limit cycles, like period doubling and chaos. In additions, we propose the prototype-4 R¨ossler system in fractional version with short memory operator. Then, a proposed non-autonomous fractional order Rossler blinking system is introduced. Numerical simulations are employed to confirm the existence of ghost attractors at specific cases which involve very fast switching time between two composing autonomous fractional subsystems. It is found that the presented fractional order blinking system is very sensitive to system parameters, initial conditions and stochastic process parameters. Thus, the induced chaotic ghost attractor is utilized in a suggested ghost attractor-based chaotic image encryption scheme for first time. Finally, a detailed security analysis is carried out which reveals that the proposed image cryptosystem is immune against different types of attacks such as differential attacks, brute force attacks, cropping and statistical attacks. Concluding remarks and suggested future work are given in chapter four.