This paper proposed a fractional model for the flow rate and characteristic of the impurity of order α, β(0<α, β≤1) respectively, which describes one dimensional dynamical flows of electrically conducting fluid. In this model fractional derivatives are described in the Caputo sense. The beauty of the paper is residual analysis which shows that our approximate solution converges very rapidly to ...

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...

Using the generalized Kolmogorov-Feller equation with long-range interaction, we obtain kinetic equations with fractional derivatives with respect to coordinates. The method of successive approximations with the averaging with respect to fast variable is used. The main assumption is that the correlator of probability densities of particles to make a step has a power-law dependence. As a result,...

The theory of derivatives and integrals of fractional in fractional calculus have found enormousapplications in mathematics, physics and engineering so for that reason we need an efficient and accurate computational method for the solution of fractional differential equations. This paper presents a numerical method for solving a class of linear and nonlinear multi-order fractional differential ...

We discuss a dynamic procedure that makes fractional derivatives emerge in the time asymptotic limit of non-Poisson processes. We find that two-state fluctuations, with an inverse power-law distribution of waiting times, finite first moment, and divergent second moment, namely, with the power index mu in the interval 2<mu<3 , yield a generalized master equation equivalent to the sum of an ordin...

The theory of fractional calculus goes back to the beginning of the theory of differential calculus, but its application received attention only recently. In the area of automatic control some work was developed, but the proposed algorithms are still in a research stage. This paper discusses a novel method, with two degrees of freedom, for the design of fractional discrete-time derivatives. The...

In the paper, we present some applications and features related with the new notions of fractional derivatives with a time exponential kernel and with spatial Gauss kernel for gradient and Laplacian operators. Specifically, for these new models we have proved the coherence with the thermodynamic laws. Hence, we have revised the standard linear solid of Zener within continuum mechanics and the m...

In this paper, we tried to evaluate the fractional derivatives by using the Chebyshev series expansion. We discuss the indefinite quadrature rule to estimate the fractional derivatives of Riemann-Liouville type.

Fractional calculus has recently attracted much attention in the literature. In particular, fractional derivatives are widely discussed and applied in many areas. However, it is still hard to develop numerical methods for fractional calculus. In this paper, based on Fourier series and Taylor series technique, we provide some numerical methods for computing and simulating fractional derivatives ...