Modeling and analysis of competition model of bank data with fractal-fractional Caputo-Fabrizio operator

The present paper consider a newly introduced operator known as fractal-fractional where the fractional operator considered is Caputo-Fabrizio. We consider a competition system and propose the field data of banks for 2004–2014 of Indonesia banks of the type rural and commercial. The model with fractal-fractional operator known as fractal-fractional Caputo-Fabrizio derivative is formulated and show their analysis. We give a novel method to solve the model numerically and present the graphical results. We consider different values of the fractal and fractional order parameters and compare the results with integer order fitting for real data. We show keeping fractal order fix and varying fractional order, keeping fractional order fix and varying fractal, varying both fractional and fractal order for fixed values, varying values arbitrarily, and for long term, we achieve better results for fitting than that of integer order for commercial and rural data. This new definition of fractal-fractional in the form of Caputo-Fabrizio derivative provide better results than that of the ordinary integer order.