Calculus of variations with fractional derivatives and fractional integrals

2009/07/06 by Ricardo Almeida, Delfim F. M. Torres · 6 citations
Mathematics · Physics and Astronomy · #Applied mathematics #Calculus (dental) #Euler's formula #Fractional Differential Equations Solutions #Fractional calculus #Iterative Methods for Nonlinear Equations #Mathematical analysis #Mathematics #Nonlinear Differential Equations Analysis #Pure mathematics #math-ph #math.MP #math.OC #msc:26A33 #msc:49K05

paper · pdf · doi:10.1016/j.aml.2009.07.002

published as Applied Mathematics Letters 22 (2009) 1816--1820 · Accepted (July 6, 2009) for publication in Applied Mathematics Letters

arxiv created 2009/07/06 · openalex publication_date 2009/07/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We prove Euler-Lagrange fractional equations and sufficient optimality conditions for problems of the calculus of variations with functionals containing both fractional derivatives and fractional integrals in the sense of Riemann-Liouville.

Citations

• Fractional conservation laws in optimal control theory
• ON FRACTIONAL INTEGRALS AND DERIVATIVES
• Necessary optimality conditions for fractional action‐like integrals of variational calculus with Riemann–Liouville derivatives of order (α, β)
• Fractional Differential Equations

Cited by

• Combined fractional variational problems of variable order and some computational aspects
• Duality for the left and right fractional derivatives
• Fractional Calculus on Time Scales
• Fractional Calculus of Variations in Terms of a Generalized Fractional Integral with Applications to Physics
• Fractional calculus of variations for a combined Caputo derivative
• Fractional Order Version of the Hamilton–Jacobi–Bellman Equation

Related

• The Euler-Lagrange and Legendre Necessary Conditions for Fractional Calculus of Variations
• Generalized Fractional Calculus of Variations
• Fractional Calculus of Variations in Terms of a Generalized Fractional Integral with Applications to Physics
• Necessary conditions to a fractional variational problem
• On a New Class of Fractional Calculus of Variations and Related Fractional Differential Equations