I am pleased to share our latest publication in the Revista de la Unión Matemática Argentina. The paper is entitled: "On fractal multiplicative derivatives and their applications". In this work, we develop a fractal multiplicative calculus framework and investigate its main theoretical and applied aspects. We introduce a new fractal multiplicative derivative and establish its fundamental properties, including a Leibniz-type rule. In addition, we study a corresponding multiplicative integral operator and analyze its key features. The proposed framework is then applied to the study of fractal and multiplicative differential equations, as well as to multiplicative function spaces and problems in the calculus of variations. As a relevant application, we formulate a fractal multiplicative version of the Gompertz growth model. Furthermore, numerical experiments based on real data demonstrate that the proposed model provides an improved fit compared to other generalized approaches. These results highlight the effectiveness and flexibility of fractal multiplicative calculus in modeling complex systems with nonstandard growth dynamics.

Many thanks to Professor Juan Eduardo Nápoles Valdes for the collaboration.

DOI

Please note that this is the Early View version of the paper. I will share the final published version once it becomes available.

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