الفهرس 
IntroductionOnly 14 pages are availabe for public view
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Abstract
A complex adaptive system (CAS) is studied. We motivated the use of fractional differential equations (FDE) and fractional partial differential equations (FPDE) in CAS because they naturally include memory effects which should not be neglected in CAS. Also they generalize ODE and PDE which are used to study CAS. Also we studied evolutionary game theory (EGT), replicator equation, the hawk-dove (HD) game, the Prisoner’s Dilemma (PD) game, Turing instability and gave examples of biological systems. The existence and uniqueness of the initial value problem of the fractional-order logistic equation is studied and then studied the equilibrium points and their asymptotic stability of the fractional-order logistic equation and gave the numerical solution of the fractional-order logistic equation We generalized the replicator equation to the fractional-order differential equation and then studied the fractional hawk-dove (HD) game and the fractional Prisoner’s Dilemma (PD) game, where we studied the equilibrium points and their asymptotic stability and the numerical solution of HD game and PD game. We studied the existence and uniqueness of the initial value problem of the fractional-order predator-prey system and then studied the equilibrium points and their asymptotic stability of the fractional-order predator-prey system and gave the numerical solution of the fractional-order predatorprey system. For studying the equilibrium points and their asymptotic stability of the fractional order differential equations, we found that the fractional order is more stable than the integer order one and the numerical simulations support this result. We studied the equilibrium points and their asymptotic stability of the fractional-order partial differential equation and then studied the equilibrium points and their asymptotic stability of the fractional-order partial logistic equation and of the fractional-order partial predator-prey system. and gave the numerical solution of them. Also the Fractional-order Turing instability is studied. Four papers from this thesis are published in specialized scientific world journals.