Más allá de un instante. Memoria y no localidad en cálculo fraccionario

Abstract

Fractional calculus emerges as a natural extension of classical calculus, extending its ability to model phenomena that depend not only on the current state, but also on the past and the environment. Unlike traditional models, fractional derivatives allow for capturing memory and spatial non-locality effects. Using a literary metaphor, the text argues that many real-world processes cannot be understood without considering their history. Some historical origins of fractional calculus and its current applications in modeling physical and technological phenomena are discussed. The aim is to show how these mathematical tools offer a deeper and more flexible view of the world, in which memory and non-local influences play a fundamental role.