2017/03/27 by Dina Tavares, Ricardo Almeida, Delfim F. M. Torres · 1 citation
Computer Science · Mathematics · #Differential equation #Fractional Differential Equations Solutions #Fractional calculus #Nonlinear Differential Equations Analysis #Optimization and Variational Analysis #Order (exchange) #Type (biology) #Variable (mathematics) #Variables #math.OC #msc:26A33 #msc:34A08 #msc:49K05 #msc:49K10
paper · pdf · doi:10.3934/dcdss.2018009
published as Discrete Contin. Dyn. Syst. Ser. S 11 (2018), no. 1, 143--154 · This is a preprint of a paper whose final and definite form is with 'Discrete and Continuous Dynamical Systems -- Series S' (DCDS-S), ISSN 1937-1632 (print), ISSN 1937-1179 (online), available at [https://www.aimsciences.org/journals/home.jsp?journalID=15]. Paper Submitted 30-July-2016; Revised 03-Feb-2017; Accepted 27-March-2017
arxiv created 2017/03/27 · openalex created_date 2017/04/07 · openalex publication_date 2017/10/10 · arxiv updated 2017/10/12 · openalex updated_date 2026/08/05
We study fractional variational problems of Herglotz type of variable order. Necessary optimality conditions, described by fractional differential equations depending on a combined Caputo fractional derivative of variable order, are proved. Two different cases are considered: the fundamental problem, with one independent variable, and the general case, with several independent variables. We end with some illustrative examples of the results of the paper.