Search

In this work, we introduce a definition of a local fractional derivative and a fractional integral of order alfa > 0 (where this parameter does not need to be integer), with which we overcome some deficiencies of known local derivatives, conformable or not. This definition allows to compute fractional derivatives of functions defined on any open set on the real line (and not just on the positive half-line). Moreover, we extend some classical results to the context of fractional derivatives. Also, applications of the fractional derivative through the direct and inverse problems are shown, as well as the feasibility of the fractional calculus in real and simulated problems. Programa de Doctorado en Ingeniería Matemática por la Universidad Carlos III de Madrid Presidente: Domingo de Guzmán Pestana Galván.- Secretario: Ana Portilla Ferreira.- Vocal: Ana Granados Sanandrés

Entre los objetivos de las Matemáticas está el tratar de describir y predecir eventos que suceden en el mundo real; esto esencialmente se logra a través de representaciones matemáticas. Muchas de las leyes de la naturaleza pueden estudiarse mediante sistemas de ecuaciones diferenciales, en las cuales se ven involucrados parámetros que caracterizan dicho sistema. Por otro lado, al momento de incorporar datos experimentales, se presenta cierto grado de incertidumbre debido a múltiples factores asociados al sistema, entre ellos, errores de medición o de modelación. Among the objectives of Mathematics is to try to describe and predict events that happen in the real world; this is essentially achieved through mathematical representations. Many of the laws of nature can be studied through systems of di_erential equations, in which parameters that characterize this system are involved. On the other hand, when incorporating experimental data, a certain degree of uncertainty is presented due to multiple factors associated with the system, among them, errors of measurement or modeling.