School of Mathematics and Statistics;
Huazhong University of Science and Technology;
Wuhan 430074;
China;
Hubei Key Laboratory of Engineering Modeling and Scientific Computing;
Huazhong University of Science and Technology;
Wuhan 430074;
China;
fractional order system; differential-algebraic system; prey-predator bioeconomic model; singularity induced bifurcation; optimal control;