Diffusivity equation commonly used for pressure distribution prediction in porous media results from substituting equation of state and continuity equation in Navier-Stokes momentum equation. From mathematical point of view this equation format shows infinite propagation speed for pressure pulse through porous media, which is physically impossible. This issue may caused by numerous assumption...

We derive and discuss the analytical solution for the generalized time-fractional telegraph equation with the help of the Sumudu and Fourier transforms. In the process we use Green functions to derive the solution of the said differential equation.

In this paper, we consider a nonhomogeneous space-time fractional telegraph equation defined in a bounded space domain, which is obtained from the standard telegraph equation by replacing the firstor second-order time derivative by the Caputo fractional derivative Dt , α > 0; and the Laplacian operator by the fractional Laplacian (−∆) , β ∈ (0, 2]. We discuss and derive the analytical solutions...

in this paper, we propose a new method for the numerical solution of two-dimensional linear and nonlinear volterra integral equations of the first and second kinds, which avoids from using starting values. an existence and uniqueness theorem is proved and convergence isverified by using an appropriate variety of the gronwall inequality. application of the method is demonstrated for solving the ...

We present a new method based on unification of fictitious time integration (FTI) and group preserving (GP) methods. The GP is applied in numerically discretized ordinary differential equations obtained from application FTI to given partial equation (PDE). algorithm hyperbolic telegraph utilizes the Cayley transformation Pade approximations Minkowski space. It avoid...

In this paper, we approximate the solution to time-fractional telegraph equation by two kinds of difference methods: the Grünwald formula and Caputo fractional difference.

Cosmic rays (CR), constrained by scattering on magnetic irregularities, are believed to propagate diffusively. However, a well-known defect of diffusive approximation, whereby some of the particles propagate unrealistically fast, has directed interest toward an alternative CR transport model based on the “telegraph” equation. Though, its derivations often lack rigor and transparency leading to ...