Fractional differential equation

We consider the numerical solution of the Bagley-Torvik equation Ay?(t) + BD*3/2y(t) + Cy(t) = f(t), as a prototype fractional differential equation with two derivatives. Approximate solutions have recently been proposed in the book and papers of Podlubny in which the solution obtained with approximate methods is compared to the exact solution. In this paper we consider the reformulation of

We model the transport of fluid through porous media in terms of fractional diffusion equation (FDE) for the pressure (,) p x t. Potential application could be to shale gas recovery in tight porous media. Specifically, we pose the time FDE in a finite domain of length L, 0 (,), 0 , 0 t

In recent years, the application of fractional calculus in physics, continuum mechanics, signal processing, and electromagnetics, with few examples of applications in bioengineering are high lighted in the literature. The methods of fractional calculus, when defined as a Laplace, Sumudu or Fourier convolution product, are suitable for solving many problems in emerging biomedical research. The electrical properties of nerve cell membranes and the propagation of electrical signals are well characterized by differential equations of fractional order. The fractional derivative accurately describes natural phenomena that occur in such common engineering problems as heat transfer, electrode/electrolyte behavior, and sub-threshold nerve propagation. Application of fractional derivatives to viscoelastic materials establishes, in a natural way, hereditary integrals and the power law stress-strain relationship for modeling biomaterials. Fractional operations by following the original approach...