Abstract
Over the last 20 years arbitrary order calculus (better known in the literature as fractional calculus) has been developed impressively. However, in Mexico there are no solid groups devoted to its study and applications. The objetive of this work is to present the origins and development of fractional calculus, in order to encourage future researchers to venture into this very interesting area of unconventional mathematical analysis. Finally, as an example, vertical motion of a particle within a medium where resistance is proportional to speed is analized.
References
Caputo, M. (1969). Elasticità e Dissipazione. Bologna: Zanichelli.
Leibniz, G. (1859). Mathematische Schriften. Berlín: Verlag von A. Asher & Comp.
Leibniz, G. (1832). Cuarta carta a Wallis. Oeuvres complètes (tome III, 105 pp.). Paris.
Létnikov, A.V. (1868). Theory of differentiation of an arbitrary order, Mat. Sb., 3, 1–68.
Podlubny, I. (1999). Fractional Differential Equations. San Diego: Academic Press.
Oeuvres mathématiques de Riemann. París: Gauthier-villar.