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Necessary optimality conditions for fractional action‐like integrals of variational calculus with Riemann–Liouville derivatives of order (α, β)
Author(s) -
ElNabulsi Rami Ahmad,
Torres Delfim F. M.
Publication year - 2007
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.879
Subject(s) - mathematics , fractional calculus , action (physics) , calculus of variations , order (exchange) , type (biology) , euler–lagrange equation , euler's formula , calculus (dental) , mathematical analysis , pure mathematics , lagrangian , medicine , ecology , physics , dentistry , finance , quantum mechanics , economics , biology
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 (α, β), α>0, β>0, recently introduced by Cresson. Some interesting consequences are obtained and discussed. Copyright © 2007 John Wiley & Sons, Ltd.