in this paper, the dynamical behavior of an axially moving string modeled by fractional derivative is investigated. the governing equation represented motion is solved by the method of multiple scales. considering principal parametric resonance, the stability boundaries for string with simple supports are obtained. numerical results indicate the effects of fractional damping on stability.

a computational method for numerical solution of a nonlinear volterra and fredholm integro-differentialequations of fractional order based on chebyshev cardinal functions is introduced. the chebyshev cardinaloperational matrix of fractional derivative is derived and used to transform the main equation to a system ofalgebraic equations. some examples are included to demonstrate the validity and ...

in this paper we introduce a type of fractional-order polynomials basedon the classical chebyshev polynomials of the second kind (fcss). also we construct the operationalmatrix of fractional derivative of order $ gamma $ in the caputo for fcss and show that this matrix with the tau method are utilized to reduce the solution of some fractional-order differential equations.

‎‎in this paper‎, ‎the existence and uniqueness of positive solutions for a class of nonlinear initial value problem for a finite fractional difference equation obtained by constructing the upper and lower control functions of nonlinear term without any monotone requirement‎ .‎the solutions of fractional difference equation are the size of tumor in model tumor growth described by the gompertz f...

in this article, we apply two new fixed point theorems to investigate the existence of mild solutions for a nonlocal fractional cauchy problem with an integral initial condition in banach spaces.

The performance of water flooding can be investigated by using either detail numerical modeling or simulation, or simply through the analytical Buckley-Leverett (BL) model. The Buckley-Leverett analytical technique can be applied to one-dimensional homogeneous systems. In this paper, the impact of heterogeneity on water flooding performance and fractional flow curve is investigated. First, a ba...

The Liouville equation, first Bogoliubov hierarchy and Vlasov equations with derivatives of non-integer order are derived. Liouville equation with fractional derivatives is obtained from the conservation of probability in a fractional volume element. This equation is used to obtain Bogoliubov hierarchy and fractional kinetic equations with fractional derivatives. Statistical mechanics of fracti...

We consider the initial value problem for some nonlinear hyperbolic and dispersive systems in one space dimension. Combining the classical energy method and the smoothing estimates for the Airy equation, we guarantee the time local well-posedness for this system. We also discuss the extension of our results to more general hyperbolic-dispersive system.

We prove an endpoint multilinear estimate for the X spaces associated to the periodic Airy equation. As a consequence we obtain sharp local well-posedness results for periodic generalized KdV equations, as well as some global well-posedness results below the energy norm.

Asymptotic approximations are developed for zeros of the solutions Gi(z) and Hi(z) of the inhomogeneous Airy differential equation w′′ − zw = ± 1 π . The solutions are also called Scorer functions. Tables are given with numerical values of the zeros. 2000 Mathematics Subject Classification: 33C10, 41A60, 30E10, 30C15.