Abstract
Natural symmetries exist in several processes of chemistry, physics, and biology. Symmetries possess interesting dynamical characteristics that cannot be seen in non-symmetric systems. The present paper investigates the competition between two banking systems, rural and commercial, in Indonesia, in parameterized fractional order Caputo derivative. A novel numerical method is used to discretize the competition system using the real data of rural and commercial banks in Indonesia for the period 2004-2014. The new scheme is more suitable and reliable for data fitting results and has good accuracy. The integer model is formulated in Caputo derivative and their stability results are presented. With the available parameters, the data for the model is analyzed using various scenarios. We shall compare the result with the previous method used in the literature and show that the present method is better than the previous method in the literature. It is shown that fractional order alpha and the parameter rho involved in the numerical scheme provide excellent fitting.