2017/04/21 by Dina Tavares, Ricardo Almeida, Delfim F. M. Torres · 2 citations
Engineering · Mathematics · #Advanced Control Systems Design #Applied mathematics #Derivative (finance) #Fractional Differential Equations Solutions #Fractional calculus #Mathematical analysis #Mathematical optimization #Mathematics #Nonlinear Differential Equations Analysis #Order (exchange) #Physics #State variable #Transversality #Variable (mathematics) #math.OC #msc:26A33 #msc:34A08 #msc:49K05
paper · pdf · doi:10.1016/j.cam.2017.04.042
published as J. Comput. Appl. Math. 339 (2018), 374--388 · This is a preprint of a paper whose final and definite form is with 'Journal of Computational and Applied Mathematics', ISSN: 0377-0427. Submitted 15-Feb-2017; Revised 17-Apr-2017; Accepted 21-Apr-2017
arxiv created 2017/04/21 · openalex publication_date 2017/05/02 · arxiv updated 2018/04/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study two generalizations of fractional variational problems by considering higher-order derivatives and a state time delay. We prove a higher-order integration by parts formula involving a Caputo fractional derivative of variable order and we establish several necessary optimality conditions for functionals containing a combined Caputo derivative of variable fractional order. Because the endpoint is considered to be free, we also deduce associated transversality conditions. In the end, we consider functionals with a time delay and deduce corresponding optimality conditions. Some examples are given to illustrate the new results. Computational aspects are discussed using the open source software package Chebfun.