This paper deals with a newly born fractional derivative and integral on time scales. A chain rule is derived, and the given indefinite integral is being discussed. Also, an application to the traffic flow problem with a fractional Burger's equation is presented.
Abstract. This work, deals with a fractional optimal control problem (in the Riemann-Liouville sense). An analytic description of an initial value appears in the constraint of the optimal control problem is presented and some sufficient and necessary conditions for the given initial value is obtained. Making use of an auxiliary variable together with the optimal control law, the given problem is converted into a system of ordinary integro-differential equations. Then using the Adomian decomposition method, an approximate solution is illustrated.
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