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• Application of newly operator called fractal-fractional to a bank data is presented. • A novel numerical approach for the solution of fractal-fractional model is shown. • Data analysis and its simulations for various values of fractal-fractional orders. • Fractal and fractional orders gives best setting for parameters. A novel investigation for banking data through mathematical model with a novel operator known as fractal-fractional in the sense of Caputo derivative is presented. We present the comparative analysis of rural and commercial banks data of Indonesia for the years 2004–2014 through a differential equation. We estimate some reasonable set of parameters for both the data and then present the numerical results. We show that the solution of the fractal-fractional model exists and unique. A novel numerical procedure for the fractal-fractional model with details is presented. Various graphical results are presented when considering the values of fractal and fractional order. We show that varying both the orders we have best fitting to the data. [ABSTRACT FROM AUTHOR]