In this paper, a method of separating variables is effectively implemented for solving a time-fractional telegraph equation (TFTE). We discuss and derive the analytical solution of the TFTE with three kinds of nonhomogeneous boundary conditions, namely, Dirichlet, Neumann and Robin boundary conditions. © 2007 Elsevier Inc. All rights reserved.

An application of the Exp-function method to search for exact solutions of nonlinear differential equations is analyzed. Typical mistakes of application of the Exp-function method are demonstrated. We show it is often required to simplify the exact solutions obtained. Possibilities of the Exp-function method and other approaches in mathematical physics are discussed. The application of the sing...

Abstract We present a computer-assisted approach to prove the existence of Hopf bubbles and degenerate bifurcations in ordinary delay differential equations. apply method rigorously investigate these nonlocal orbit structures FitzHugh–Nagumo equation, extended Lorenz-84 model time-delay SI model.

The specific solutions of the telegraph equation for 3D space are constructed. These solutions enable us to obtain the wavefunctions which are akin to the Bessel-Gauss wave modes. The solutions of the homogeneous and inhomogeneous equations are compared. The application of the obtained wave structures to the description of the electromagnetic fields in a special case of inhomogeneity of the med...

In this paper, an alternative method for accurately and efficiently modeling for the onedimensional Telegraph equation that combines classical and integral boundary conditions is presented. New matrix formulation technique with arbitrary polynomial bases is proposed for the numerical/analytical solution of this kind of partial differential equation. Not only the exact solutions have been achiev...