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A Riesz difference is defined by the use of the Riemann-Liouville differences on time scales. Then the definition is considered for discrete fractional modelling. A lattice fractional equation method is proposed among which the space variable is defined on discrete domains. Finite memory effects are introduced into the lattice system and the numerical formulae are given. Adomian decomposition method is adopted to solve the fractional partial difference equations numerically. [ABSTRACT FROM AUTHOR]

From the local fractional calculus viewpoint, Poisson and Laplace equations were presented in this paper. Their applications to the electrostatics in fractal media are discussed and their local forms in the Cantor-type cylindrical coordinates are also obtained. [ABSTRACT FROM AUTHOR]

A new impulsive multi-orders fractional differential equation is studied. The existence and uniqueness results are obtained for a nonlinear problem with fractional integral boundary conditions by applying standard fixed point theorems. An example for the illustration of the main result is presented. [ABSTRACT FROM AUTHOR]

We suggest a new model of the scale conservation equation in the mathematical theory of vehicular traffic flow on the fractal network based on the local fractional calculus. [ABSTRACT FROM AUTHOR]

Equations of motion for Einstein’s field in fractional dimension of 4 spatial coordinates are obtained. It is shown that time dependent part of Einstein’s wave function is single valued for only 4-integer dimensional space. [ABSTRACT FROM AUTHOR]

The local free coordinates on the constraint surface are obtained within symplectic projector method when the constraints are linearly dependent. One example is investigated in details. [ABSTRACT FROM AUTHOR]

The irregular constrained systems are investigated within Hamilton-Jacobi formalism. For this type of systems the equivalence of Hamilton-Jacobi formalism and Lagrangian formulation is presented and one example is analyzed in details. [ABSTRACT FROM AUTHOR]

Fractional Euler-Lagrange equations are investigated in the presence of Grassmann variables. The fractional Hamiltonian and the path integral of the fractional supersymmetric classical model are constructed. [ABSTRACT FROM AUTHOR]

Abstract An extension of Riewe’s fractional Hamiltonian formulation is presented for fractional constrained systems. The conditions of consistency of the set of constraints with equations of motion are investigated. Three examples of fractional constrained systems are analyzed in details. [ABSTRACT FROM AUTHOR]

Abstract Metafluid dynamics was investigated within Hamilton-Jacobi formalism and the existence of the hidden gauge symmetry was analyzed. The obtained results are in agreement with those of Faddeev-Jackiw approach. [ABSTRACT FROM AUTHOR]

We establish that, under some simple integral conditions regarding the nonlinearity, the (1 + a)-order fractional differential equation 0Dat(x') + f(t, x) = 0, t > 0, has a solution x\in C([0,+\infty ),\mathbb {R})\cap C^{1}((0,+\infty ),\mathbb {R}), with \lim \limits _{t\searrow 0}[t^{1-\alpha }x^{\prime }(t)]\in \mathbb {R}, which can be expanded asymptotically as a + bta + O(ta [?] 1) when t - +[?] for given real numbers a, b. Our arguments are based on fixed point theory. Here, 0Dat designates the Riemann-Liouville derivative of order a [?] (0, 1). [ABSTRACT FROM AUTHOR]

This paper presents a fractional Dirac equation and its solution. The fractional Dirac equation may be obtained using a fractional variational principle and a fractional Klein-Gordon equation; both methods are considered here. We extend the variational formulations for fractional discrete systems to fractional field systems defined in terms of Caputo derivatives. By applying the variational principle to a fractional action S, we obtain the fractional Euler-Lagrange equations of motion. We present a Lagrangian and a Hamiltonian for the fractional Dirac equation of order a. We also use a fractional Klein-Gordon equation to obtain the fractional Dirac equation which is the same as that obtained using the fractional variational principle. Eigensolutions of this equation are presented which follow the same approach as that for the solution of the standard Dirac equation. We also provide expressions for the path integral quantization for the fractional Dirac field which, in the limit a - 1, approaches to the path integral for the regular Dirac field. It is hoped that the fractional Dirac equation and the path integral quantization of the fractional field will allow further development of fractional relativistic quantum mechanics. [ABSTRACT FROM AUTHOR]

The fractional variational principles within Riemann-Liouville fractional derivatives in the presence of delay are analyzed. The corresponding Euler-Lagrange equations are obtained and one example is analyzed in detail. [ABSTRACT FROM AUTHOR]