Browsing by Author "Avkar, T"

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Citation - WoS: 2
Fractional Euler-Lagrange Equations for Constrained Systems
(Amer inst Physics, 2004) Avkar, Tansel; Avkar, T; Baleanu, D; Baleanu, Dumitru; Matematik
The fractional calculus is the name for the theory of integrals and derivatives of arbitrary order, which generalize the notions of n-fold integration and integer-order differentiation. Differential equations of fractional order appear in certain applied problems and in theoretical researches. In this paper, the Euler-Lagrange equations of the Lagrangians linear in velocities were derived using the fractional calculus. Two examples of constrained systems possessing a gauge invariance are investigated in details, the explicit solutions of Euler-Lagrange equations are obtained, and the recovery of the classical results is discussed.
Citation - WoS: 168
Citation - Scopus: 187
Lagrangians With Linear Velocities Within Riemann-Liouville Fractional Derivatives
(Soc Italiana Fisica, 2004) Baleanu, D; Avkar, T
Lagrangians linear in velocities were analyzed using the fractional calculus and the Euler-Lagrange equations were derived. Two examples were investigated in details; the explicit solutions of Euler-Lagrange equations were obtained and the recovery of the classical results was discussed.