On Fractal Operators: Theory and Applications

ABSTRACT Fractal calculus is a powerful new mathematical tool that helps model systems which are too complex, irregular, or high‐dimensional for traditional calculus to handle. This work introduces several foundational tools related to fractal derivatives, including a Gronwall's inequality adapted to the fractal setting. Also, we show that fractal derivatives can, in certain cases, more accurately model real‐world phenomena than traditional derivatives (classical and Caputo differential equations). In particular, we show the good fit of the fractal model in predicting empirical data on the values of Mexico's gross domestic product.