数学物理学报(英文版) ›› 2012, Vol. 32 ›› Issue (2): 619-630.doi: 10.1016/S0252-9602(12)60043-5

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ISOPERIMETRIC PROBLEMS OF THE CALCULUS OF VARIATIONS WITH FRACTIONAL DERIVATIVES

Ricardo Almeida1, Rui A. C. Ferreira1,2, Delfim F. M. Torres1   

  1. 1. Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal;
    2. Department of Mathematics, Faculty of Engineering and Natural Sciences, Lusophone University of Humanities and Technologies, 1749-024 Lisbon, Portugal
  • 收稿日期:2009-10-14 修回日期:2010-06-30 出版日期:2012-03-20 发布日期:2012-03-20
  • 基金资助:

    This work was supported by FEDER funds through COMPETE — Operational Programme Factors of Competitiveness (“Programa Operacional Factores de Competitividade”) and by Portuguese funds through the Center for Research and Development in Mathematics
    and Applications (University of Aveiro) and the Portuguese Foundation for Science and Technology (“FCT —Funda¸c˜ao para a Ciˆencia e a Tecnologia”), within project PEst-C/MAT/UI4106/2011 with COMPETE number FCOMP-01-0124-FEDER-022690.

ISOPERIMETRIC PROBLEMS OF THE CALCULUS OF VARIATIONS WITH FRACTIONAL DERIVATIVES

Ricardo Almeida1, Rui A. C. Ferreira1,2, Delfim F. M. Torres1   

  1. 1. Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal;
    2. Department of Mathematics, Faculty of Engineering and Natural Sciences, Lusophone University of Humanities and Technologies, 1749-024 Lisbon, Portugal
  • Received:2009-10-14 Revised:2010-06-30 Online:2012-03-20 Published:2012-03-20
  • Supported by:

    This work was supported by FEDER funds through COMPETE — Operational Programme Factors of Competitiveness (“Programa Operacional Factores de Competitividade”) and by Portuguese funds through the Center for Research and Development in Mathematics
    and Applications (University of Aveiro) and the Portuguese Foundation for Science and Technology (“FCT —Funda¸c˜ao para a Ciˆencia e a Tecnologia”), within project PEst-C/MAT/UI4106/2011 with COMPETE number FCOMP-01-0124-FEDER-022690.

摘要:

In this article, we study isoperimetric problems of the calculus of variations with left and right Riemann-Liouville fractional derivatives. Both situations when the lower bound of the variational integrals coincide and do not coincide with the lower bound of the fractional derivatives are considered.

关键词: Calculus of variations, fractional derivatives, isoperimetric problems

Abstract:

In this article, we study isoperimetric problems of the calculus of variations with left and right Riemann-Liouville fractional derivatives. Both situations when the lower bound of the variational integrals coincide and do not coincide with the lower bound of the fractional derivatives are considered.

Key words: Calculus of variations, fractional derivatives, isoperimetric problems

中图分类号: 

  • 49K05