Una introducción al cálculo fraccional con aplicaciones en la física Academic Article in Scopus uri icon

abstract

  • This work offers an introduction to the fundamental concepts of fractional calculus, highlighting the most commonly used definitions of the fractional derivative and emphasizing its properties and applications. In particular, the fractional Fourier derivative is analyzed, underscoring its relative simplicity for numerical implementation, and Matlab and Python code based on spectral methods for its calculation is presented. Furthermore, key applications of fractional derivatives in physics are explored, such as their use in optical beams, viscoelastic structures, quantum mechanics, and the fractional harmonic oscillator. As a complement, the fundamentals of the Mittag-Leffler function, widely used in fractional calculus, are introduced. Finally, potential future applications of fractional calculus are discussed, highlighting its relevance in various areas of physics. © 2026 Sociedad Mexicana de Fisica. All rights reserved.

publication date

  • January 1, 2026