2011/02/18 by Natália Martins, Natalia Martins, Delfim F. M. Torres
Computer Science · Mathematics · #Applied mathematics #Calculus (dental) #Calculus of variations #Euler's formula #Euler–Lagrange equation #Fractional Differential Equations Solutions #Function (biology) #Generalization #Lagrangian #Mathematical analysis #Mathematics #Nonlinear Differential Equations Analysis #Optimization and Variational Analysis #Pure mathematics #Type (biology) #Variable (mathematics) #Variety (cybernetics) #math.OC #msc:34N05 #msc:39A12 #msc:49K15
paper · pdf · doi:10.1016/j.camwa.2011.02.022
published as Comput. Math. Appl. 61 (2011), no. 9, 2424--2435 · Submitted 25-Jul-2010; revised 27-Nov-2010; accepted 16-Feb-2011; for publication in Computers and Mathematics with Applications
arxiv created 2011/02/18 · openalex publication_date 2011/03/13 · arxiv updated 2011/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We prove necessary optimality conditions of Euler-Lagrange type for generalized problems of the calculus of variations on time scales with a Lagrangian depending not only on the independent variable, an unknown function and its delta derivative, but also on a delta indefinite integral that depends on the unknown function. Such kind of variational problems were considered by Euler himself and have been recently investigated in [Methods Appl. Anal. 15 (2008), no. 4, 427-435]. Our results not only provide a generalization to previous results, but also give some other interesting optimality conditions as special cases.