Papers by Keyword: Fractional Derivative

Abstract: This paper, with fractional calculus theory and Maple as tools, takes cigarettes as porous media to establish a fractional model describing filtration effect of cigarette filter tip, and explains the relationship between the functions of filter tip and filter materials, and reveals the relationship between the role of filter tip and the filter length. The results show that the improvement of the absorption rate of toxics and increasement of filter length can exponentially improve the filtering effect. Moreover, the speed lowering of the smoke smog spreading can also improve the filtering effect.

Abstract: A numerical method is proposed for calculating the fractional order derivative and successfully resolving the integrand singularity problem based on Zhang-Shimizu algorithm. And then a method is developed to calculate the twice nonlinear fractional derivative, numerical examples demonstrate the numerical method with high precision and good stability.

Abstract: FRPhas been widely used in the strengtheningof RC structures because of its low density, high strength and anti-corrosion. Long term performance ofFRP/concrete interface is one of the keys for its successful engineering application, and however it has notbeen well studied. In this article a fractional derivative rheological model was proposed which is able to characterize the complicated creepdeformation of epoxy FRP/concreteinterface layer with simple expression. Numerical study revealed thatinterfacial creep might lead to notable stress redistribution and largeinterfacial deformation has possibility to cause weakening of FRPstrengthening.

Abstract: A single pile in soil is modeled as a vertical circular elastic prismatic bar, and the soil around the pile is regarded as transversely isotropic medium. The relationship between stress and displacement of the soil is described by fractional derivative viscoelastic model. Ignoring the radial and vertical displacement, the torsional vibration equation of the soil is built. It is solved by using the method of separation of variables and the boundary conditions of the soil. The torsional vibration of the single pile is also obtained. The torsional complex stiffness at pile head is investigated in particular. The results indicate that anisotropic parameters and model parameters of the soil have effects on the torsional complex stiffness, and the influence rules are different with the homogeneous soil.

Abstract: Dynamic behaviour of a nonlinear plate embedded in a fractional derivative viscoelastic medium and subjected to the conditions of the combinational internal resonances of the additive and difference types has been studied by Rossikhin and Shitikova in [1]. Nonlinear equations, the linear parts of which occur to be coupled, were solved by the method of multiple time scales. A new approach proposed in [2] allows one to uncouple the linear parts of equations of motion of the plate, while the same method, the method of multiple time scales, has been utilized for solving nonlinear equations. The new approach enables one to find an additional combinational resonance of the additive-difference type, as well as to solve the problems of vibrations of thin bodies more efficiently.

Abstract: In this work, we describe the radial basis functions for solving the time fractional partial differential equations defined by Caputo sense. These problems can be discretized in the time direction based on finite difference scheme and is continuously approximated by using the radial basis functions in the space direction which achieves the semi-discrete solution. Numerical results accuracy the efficiency of the presented method.

Abstract: In vibration process, viscoelastic isolators’ temperature will rise due to energy dissipation, especially when the isolators have high damping characteristics. First, for the arbitrary loadings, the thermomechanical coupling model and the corresponding difference form are established based on the five-parameter fractional derivative model. Then, for the steady-state harmonic inputs, which is very common in engineering application, the derived model is significantly simplified by Fourier transformation. Finally, the proposed model is verified by experiments and shows a reasonable agreement with measured data.

Abstract: Dynamic behaviour of a nonlinear plate embedded in a fractional derivative viscoelastic medium and subjected to the conditions of the internal resonances two-to-one has been studied by Rossikhin and Shitikova in [1]. Nonlinear equations, the linear parts of which occur to be coupled, were solved by the method of multiple time scales. A new approach proposed in this paper allows one to uncouple the linear parts of equations of motion of the plate, while the same method, the method of multiple time scales, has been utilized for solving nonlinear equations. The new approach enables one to find a new type of the internal resonanse, i.e., one-to-one-to-two, as well as to solve the problems of vibrations of thin bodies more efficiently.

Abstract: In this paper, based on the fractional model, we present an investigation on the couette flow of a generalized Oldroyd-B fluid within an infinite cylinder subject to a time-dependent shear stress which is affected by the internal constantly decelerated pressure gradient. By using the fractional derivatives Laplace and finite Hankel transforms, the obtained solutions for the velocity field and shear stress, written in terms of generalized R function, are presented the similar characteristics with Newtonian and non-Newtonian fluids. Moreover, the effects of various parameters are systematically analyzed.

Abstract: In this paper, a new five-dimensional hyperchaotic system by introducing two additional states feedback into a three-dimensional smooth chaotic system. With three nonlinearities, this system has more than one positive Lyapunov exponents. Based on the fractional derivative theory, the fractional-order form of this new hyperchaotic system has been investigated. Through predictor-corrector algorithm, the system is proved by numerical simulation analysis. Simulation results are provided to illustrate the performance of the fractional-order hyperchaotic attractors well.