In the paper, a fractional optimal control model is constructed for a simple cash balance problem by introducing two new factors the net profit of firms and the long-term memory of the problem. The long-term memory, described by the fractional derivative of Caputo type, is characterized by a memory kernel that satisfies the law of power decline. Using the minimization sequence methods, together with techniques of nonlinear analysis, the existence of the optimal solution is obtained. Through theoretical analysis and numerical simulation, it is concluded that the strength of memory is described by the size of α, the order of the fractional derivative of cash and securities balances, and further comes to the conclusion that the smaller the value, the stronger the memory, and vice versa. Moreover, it also reveals that the memory of the problem makes it sticky, the inertia to preserve it in the previous state, which leads to a change in the balance of cash and securities being flat rather than sharp, and the total balance of cash and securities decreases with the enhancement of memory. Additionally, it suggests that when α reaches 1, the memory weakens and the viscosity becomes tinier, and the fractional model of order α tends to the integer one under α=1, which is a Markov process without memory, and at this point the model is no longer viscous. Besides that, in another perspective, the parameter α can be defined as decision makers’ reliance on historical data and experience, under which hypothesis the value of α can be used to measure the conservatism of policymakers. It is consistent with the actual, and shows the rationality and validity of the fractional model from the side.