Fractional variational calculus with classical and combined Caputo derivatives

2011/01/15 by Tatiana Odzijewicz, Agnieszka B. Malinowska, Delfim F. M. Torres · 4 citations
Mathematics · #Applied mathematics #Calculus (dental) #Calculus of variations #Computer science #Derivative (finance) #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #Euler–Lagrange equation #Extension (predicate logic) #Fractional Differential Equations Solutions #Fractional calculus #Isoperimetric inequality #Lagrangian #Mathematical analysis #Mathematics #Transversality #math.OC #msc:26A33 #msc:34A08 #msc:49K05 #msc:49K21

paper · pdf · doi:10.1016/j.na.2011.01.010

published as Nonlinear Analysis 75 (2012), no. 3, 1507-1515 · Submitted 30-Nov-2010; accepted 14-Jan-2011; for publication in Nonlinear Analysis Series A: Theory, Methods & Applications

arxiv created 2011/01/15 · openalex publication_date 2011/01/23 · arxiv updated 2011/11/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We give a proper fractional extension of the classical calculus of variations by considering variational functionals with a Lagrangian depending on a combined Caputo fractional derivative and the classical derivative. Euler-Lagrange equations to the basic and isoperimetric problems are proved, as well as transversality conditions.

Citations

• Hölderian variational problems subject to integral constraints
• Fractional Noether’s theorem in the Riesz–Caputo sense
• A fractional calculus of variations for multiple integrals with application to vibrating string
• Variational Calculus and Optimal Control
• Fractional Differential Equations

Cited by

• The DuBois–Reymond Fundamental Lemma of the Fractional Calculus of Variations and an Euler–Lagrange Equation Involving Only Derivatives of Caputo
• Fractional Calculus on Time Scales
• Fractional Calculus of Variations in Terms of a Generalized Fractional Integral with Applications to Physics
• Fractional Herglotz variational problems of variable order