Necessary optimality conditions for fractional action-like integrals of variational calculus with Riemann-Liouville derivatives of order (α, β)

被引:93
作者
El-Nabulsi, Rami Ahmad
Torres, Delfim F. M.
机构
[1] Univ Aveiro, Dept Math, Ctr Res Optimizat & Control, P-3810193 Aveiro, Portugal
[2] Jeju Natl Univ, Fac Mech Energy & Prod Engn, Dept Nucl & Energy Engn, Cheju, South Korea
关键词
fractional action-like variational approach; fractional Euler-Lagrange equations; fractional constants of motion;
D O I
10.1002/mma.879
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We derive Euler-Lagrange-type equations for fractional action-like integrals of the calculus of variations which depend on the Riemann-Liouville derivatives of order (alpha, beta), alpha > 0, beta > 0, recently introduced by Cresson. Some interesting consequences are obtained and discussed. Copyright (c) 2007 John Wiley & Sons, Ltd.
引用
收藏
页码:1931 / 1939
页数:9
相关论文
共 22 条
[11]  
FREDERICO GSF, 2006, P 2 IFAC WORKSH FRAC, P142
[12]   Lagrangian fractional mechanics - a noncommutative approach [J].
Klimek, M .
CZECHOSLOVAK JOURNAL OF PHYSICS, 2005, 55 (11) :1447-1453
[14]   Hamiltonian formulation of systems with linear velocities within Riemann-Liouville fractional derivatives [J].
Muslih, SI ;
Baleanu, D .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2005, 304 (02) :599-606
[15]  
Oldham K B, 1974, FRACTIONAL CALCULUS
[16]  
Podlubny I., 1999, Fractional Di ff erential Equations
[17]   Nonconservative Lagrangian and Hamiltonian mechanics [J].
Riewe, F .
PHYSICAL REVIEW E, 1996, 53 (02) :1890-1899
[18]  
Samko SG., 1993, Fractional Integral and Derivatives: Theory and Applications
[19]  
Srivastava H. M., 1989, UNIVALENT FUNCTIONS
[20]   Hamiltonian formalism of fractional systems [J].
Stanislavsky, AA .
EUROPEAN PHYSICAL JOURNAL B, 2006, 49 (01) :93-101