By introducing fractional exponentiation into a three-dimensional chaotic system, a jerk system with only six terms is designed. It has the property of total amplitude control, where a single non-bifurcation parameter can directly rescale all system variables without affecting the dynamics. It also features two-dimensional offset boosting, where a single parameter can realize direct offset boosting while another provides interlocked cross-dimensional offset boosting. Furthermore, this jerk system has a parameter-dominated symmetric attractor, which means that symmetric attractors appear successively as the parameter changes from positive to negative. Circuit experiments confirm the feasibility of analog fractional exponentiation using the 444 circuit and the complete control, including amplitude control and offset boosting, of the resulting system. The proposed circuit may facilitate applications of chaotic signal generators where signal versatility is important and exemplifies the generative potential of analog fractional exponentiation.