A Class Of Infinite Interval Fractional Variational Problems With Time Delay

the fractional calculus has300years old. As a relatively young discipline， it’s onlyconcerned about in the field of mathematics for a very long time. With the rapid development ofhigh-tech，it gets involved in other areas more and more，especially in the wide application ofcontrol theory，viscoelastic theory，electronic chemicals，fractal theory and so on.Fractional calculus is a promotion of the integer calculus，but the former is wider used.Switched from integer to any fraction，even irrational numbers，it has attracted the strongattention and research of the engineering and technical personnel. Accompanied the perfectconclusions and results have sprung up，the depth and difficulty are constantly increasing. Basedon the previous study，the following aspects are mainly consideved,in this the theseis:(1)The cost functional with the left and right Caputo fractional derivatives and the left andright Riemann-Liouville fractional integrals is given by(2)Integer variational problems depending on infinite-horizon and with delay.The costfunctional is given byIts Euler-Lagrange equations and transversality conditions are obtained.(3)Fractional variational problems that only contain the left Caputo fractional derivativesdepending on infinite-horizon and with delay.The cost functional study is given byIts Euler-Lagrange equations and transversality conditions are obtained.(4)Fractional variational problems that contain the left and right Caputo fractionalderivatives and the left and right Riemann-Liouville fractional integrals depending oninfinite-horizon and with delay.The cost functional is given byIts Euler-Lagrange equations and transversality conditions are obtained.(5)Laplace transform is used to obtain the analytical solution for a class of fractionallinear differential equations.