Author(s): Almeida, Ricardo
Date: 2024
Persistent ID: http://hdl.handle.net/10773/41996
Origin: RIA - Repositório Institucional da Universidade de Aveiro
Subject(s): Weighted fractional derivative; Fractional calculus of variations; Euler–Lagrange equation
In this article, we explore a variety of problems within the domain of calculus of variations, specifically in the context of fractional calculus. The fractional derivative we consider incorporates the notion of weighted fractional derivatives along with derivatives with respect to another function. Besides the fractional operators, the Lagrange function depends on extremal points. We examine the fundamental problem, providing the fractional Euler–Lagrange equation and the associated transversality conditions. Both the isoperimetric and Herglotz problems are also explored. Finally, we conclude with an analysis of the variational problem, incorporating fractional derivatives of any positive real order.
