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The main focus of this paper is to investigate the dynamics of the competition between rural and commercial bank with in the framework of fractal–fractional Atangana–Baleanu derivative sense. Initially, we take a model from literature and then utilize the real data since 2004–2014. We estimate effectively the parameters for the competition fractal–fractional model. Then, we provide a novel numerical technique for fractal–fractional model with many graphical results. We show graphical results for data fitting with the suggested operators and show that these two operators give the same results for the data fitting but varying both the values of the fractal and fractional order we have reasonable results. The results of the data fitting with these two operators are reliable and good are shown. Moreover, we present by comparing these two operators for many values of the fractal and fractional order parameters θ and α. [ABSTRACT FROM AUTHOR]