Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 16Citation - Scopus: 18On the Asymptotic Integration of a Class of Sublinear Fractional Differential Equations(Aip Publishing, 2009) Mustafa, Octavian G.; Baleanu, Dumitru; Bleanu, DumitruWe estimate the growth in time of the solutions to a class of nonlinear fractional differential equations D-0+(alpha)(x-x(0))=f(t,x) which includes D-0+(alpha)(x-x(0))=H(t)x(lambda) with lambda is an element of(0,1) for the case of slowly decaying coefficients H. The proof is based on the triple interpolation inequality on the real line and the growth estimate reads as x(t)=o(t(a alpha)) when t ->+infinity for 1>alpha>1-a>lambda>0. Our result can be thought of as a noninteger counterpart of the classical Bihari asymptotic integration result for nonlinear ordinary differential equations. By a carefully designed example we show that in some circumstances such an estimate is optimal.Article Citation - WoS: 68Citation - Scopus: 69Fractional Hamiltonian Analysis of Higher Order Derivatives Systems(Aip Publishing, 2006) Tas, Kenan; Baleanu, Dumitru; Muslih, Sami I.The fractional Hamiltonian analysis of 1+1 dimensional field theory is investigated and the fractional Ostrogradski's formulation is obtained. The fractional path integral of both simple harmonic oscillator with an acceleration-squares part and a damped oscillator are analyzed. The classical results are obtained when fractional derivatives are replaced with the integer order derivatives. (c) 2006 American Institute of Physics.