Calculus of variations with fractional derivatives and fractional integrals

被引：144
|
作者：
Almeida, Ricardo [1 ]
Torres, Delfim F. M. [1 ]
机构：
[1] Univ Aveiro, Dept Math, P-3810193 Aveiro, Portugal
来源：
APPLIED MATHEMATICS LETTERS | 2009年 / 22卷 / 12期
关键词：
Euler-Lagrange equation; Riemann-Liouville fractional derivative; Riemann-Liouville fractional integral; EULER-LAGRANGE; EQUATIONS;
D O I：
10.1016/j.aml.2009.07.002
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We prove the Euler-Lagrange fractional equations and the 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. (C) 2009 Elsevier Ltd. All rights reserved.
引用
收藏
页码：1816 / 1820
页数：5
相关论文
共 50 条
  • [1] Fractional calculus of variations for double integrals
    Odzijewicz, Tatiana
    Torres, Delfim F. M.
    BALKAN JOURNAL OF GEOMETRY AND ITS APPLICATIONS, 2011, 16 (02): : 102 - 113
  • [2] FRACTIONAL INTEGRALS AND DERIVATIVES IN q-CALCULUS
    Rajkovic, Predrag M.
    Marinkovic, Sladana D.
    Stankovic, Miomir S.
    APPLICABLE ANALYSIS AND DISCRETE MATHEMATICS, 2007, 1 (01) : 311 - 323
  • [3] ISOPERIMETRIC PROBLEMS OF THE CALCULUS OF VARIATIONS WITH FRACTIONAL DERIVATIVES
    Ricardo Almeida
    Rui A.C.Ferreira
    Delfim F.M.Torres
    ActaMathematicaScientia, 2012, 32 (02) : 619 - 630
  • [4] ISOPERIMETRIC PROBLEMS OF THE CALCULUS OF VARIATIONS WITH FRACTIONAL DERIVATIVES
    Almeida, Ricardo
    Ferreira, Rui A. C.
    Torres, Delfim F. M.
    ACTA MATHEMATICA SCIENTIA, 2012, 32 (02) : 619 - 630
  • [5] A fractional calculus of variations for multiple integrals with application to vibrating string
    Almeida, Ricardo
    Malinowska, Agnieszka B.
    Torres, Delfim F. M.
    JOURNAL OF MATHEMATICAL PHYSICS, 2010, 51 (03)
  • [6] An extended formulation of calculus of variations for incommensurate fractional derivatives with fractional performance index
    Abolhassan Razminia
    Vahid Johari Majd
    Ahmad Feyz Dizaji
    Nonlinear Dynamics, 2012, 69 : 1263 - 1284
  • [7] An extended formulation of calculus of variations for incommensurate fractional derivatives with fractional performance index
    Razminia, Abolhassan
    Majd, Vahid Johari
    Dizaji, Ahmad Feyz
    NONLINEAR DYNAMICS, 2012, 69 (03) : 1263 - 1284
  • [8] Fractional calculus of variations
    SpringerBriefs in Applied Sciences and Technology, 2015, 149 : 23 - 30
  • [9] Calculus of variations with higher order Caputo fractional derivatives
    Ferreira, Rui A. C.
    ARABIAN JOURNAL OF MATHEMATICS, 2024, 13 (01) : 91 - 101
  • [10] Fractional Calculus of Variations for Composed Functionals with Generalized Derivatives
    Almeida, Ricardo
    FRACTAL AND FRACTIONAL, 2025, 9 (03)
12345