Implement any fractional order multilayer dynamics associative neural network

The paper is to implement any fractional order multilayer dynamics associative neural network with analog fractance circuit, and to generalize traditional multilayer dynamics associative neural network being only studied in integer dimensional space into fractional dimensional space. In the first, the paper puts forward and proves a simple novel 1/2 order net-grid type analog fractance circuit model, and puts forward the symbol representing fractance circuit elements as well. In the second, it puts forward any fractional order multiplayer dynamics associative neural network being based on fractional calculus. Then it puts forward the fractional neural network's Lyapunov energy function and proves its convergence, so it also proves the stability and associational memory of the fractional neural network. In the last, the theoretical deduction and the simulative experiment fully confirm that Hopfield neural network is a special example of any fractional order multiplayer dynamics associative neural network.