Killing-Yano tensors and Nambu tensors

We present the conditions when a Killing-Yano tensor becomes a Nambu tensor. We have shown that in the flat space case all Killing-Yano tensors are Nambu tensors. In the case of Taub-NUT metric and Kerr-Newmann metric we found that a Killing-Yano tensor of order two generate a Nambu tensor of order three.Comment: content enlarged and revised,10 pages LateX, no figures, accepted for publication in Il Nuovo Ciment

Quantization of Floreanini-Jackiw chiral harmonic oscillator

The Floreanini-Jackiw formulation of the chiral quantum-mechanical system oscillator is a model of constrained theory with only second-class constraints. in the Dirac's classification.The covariant quantization needs infinite number of auxiliary variables and a Wess-Zumino term. In this paper we investigate the path integral quatization of this model using $G\ddot{u}ler's$ canonical formalism. All variables are gauge variables in this formalism. The Siegel's action is obtained using Hamilton-Jacobi formulation of the systems with constraints.Comment: 6 pages LaTeX, corrected typos, accepted for publication in Il Nuovo Cimento

New Fractional Derivatives with Nonlocal and Non-Singular Kernel: Theory and Application to Heat Transfer Model

In this manuscript we proposed a new fractional derivative with non-local and no-singular kernel. We presented some useful properties of the new derivative and applied it to solve the fractional heat transfer model.Comment: 8 Pages, The Journal Thermal Science, 201

On fractional derivatives with exponential kernel and their discrete versions

In this manuscript we define the right fractional derivative and its corresponding right fractional integral with exponential kernel. Then, we provide the integration by parts formula and we use $Q-$operator to confirm our results. The related Euler-Lagrange equations were obtained and one example is analyzed. Moreover, we formulate and discus the discrete counterparts of our results

Nambu--Poisson reformulation of the finite dimensional dynamical systems

In this paper we introduce a system of nonlinear ordinary differential equations which in a particular case reduces to Volterra's system. We found in two simplest cases the complete sets of the integrals of motion using Nambu--Poisson reformulation of the Hamiltonian dynamics. In these cases we have solved the systems by quadratures.Comment: 6 pages, latex, no figure

Integration by parts and its applications of a new nonlocal fractional derivative with Mittag-Leffler nonsingular kernel

In this manuscript we define the right fractional derivative and its corresponding right fractional integral for the recently introduced nonlocal fractional derivative with Mittag-Leffler kernel. Then, we obtain the related integration by parts formula. We use the $Q-$operator to confirm our results. The corresponding Euler-Lagrange equations are obtained and one illustrative example is discussed

On some new properties of fractional derivatives with Mittag-Leffler kernel

We establish a new formula for the fractional derivative with Mittag-Leffler kernel, in the form of a series of Riemann-Liouville fractional integrals, which brings out more clearly the non-locality of fractional derivatives and is easier to handle for certain computational purposes. We also prove existence and uniqueness results for certain families of linear and nonlinear fractional ODEs defined using this fractional derivative. We consider the possibility of a semigroup property for these derivatives, and establish extensions of the product rule and chain rule, with an application to fractional mechanics.Comment: 22 pages; accepted for publication in Communications in Nonlinear Science and Numerical Simulatio

Schr\"odinger Equation on Fractals Curves Imbedding in R3R^3

In this paper we have generalized the quantum mechanics on fractal time-space. The time is changing on Cantor-set like but space is considered as fractal curve like Von-Koch curve. The Feynman path method in quantum mechanics has been suggested on fractal curve. Using $F^{\alpha}$-calculus and Feynman path method we found the Schr\"{e}dinger on fractal time-space. The Hamiltonian operator and momentum operator has been derived. More, the continuity equation and the probability density is given in generalized formulation

On the asymptotic integration of a class of sublinear fractional differential equations

We 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 $\lambda\in(0,1)$ 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 $t\to+\infty$ for $1>\alpha>1-a>\lambda>0$. Our result can be thought of as a non--integer 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

On exact solutions of a class of fractional Euler-Lagrange equations

In this paper, first a class of fractional differential equations are obtained by using the fractional variational principles. We find a fractional Lagrangian $L(x(t)$, where $_a^cD_t^\alpha x(t))$ and $0<\alpha< 1$, such that the following is the corresponding Euler-Lagrange % \begin{equation}_tD_b^\alpha(_a^cD_t^\alpha) x(t)+ b(t,x(t))(_a^cD_t^\alpha x(t))+f(t,x(t))=0. \end{equation} % At last, exact solutions for some Euler-Lagrange equations are presented. In particular, we consider the following equations % \begin{equation}_tD_b^\alpha(_a^cD_t^\alpha x(t))=\lambda x(t), (\lambda\in R) \end{equation} % \begin{equation}_tD_b^\alpha(_a^cD_t^\alpha x(t))+g(t)_a^cD_t^\alpha x(t)=f(t), \end{equation} where g(t) and f(t) are suitable functions.Comment: 10 pages, LATEX. in press, Nonlinear Dynamic