During present investigation, a direct algebraic method based on complex solutions of nonlinear partial differential equations is developed and tested in the case of generalised Burgers–Huxley equation. The proposed scheme can be used in a wide class of nonlinear reaction–diffusion equations. These calculations demonstrate that the accuracy of the direct algebraic solutions is quite high even i...

In this paper, local and nonlocal symmetry classifications are considered for four equivalent nonlinear telegraph equations. A complete potential symmetry classification of a scalar nonlinear telegraph equation is given through the point symmetry classification of a related potential system. Six new classes of equations are shown to admit potential symmetries. The relationships between local si...

In this paper, we consider a fractional model of telegraph equation in terms of voltage and current. The fractional derivatives are taken in the Caputo sense. The numerical algorithm based on the homotopy perturbation transform method (HPTM) is applied to obtain analytic and approximate solutions of the space-time fractional telegraph equations. The HPTM is combined in the form of Laplace trans...

Abstract Aichinger’s equation is used to give simple proofs of several well-known characterizations polynomial functions as solutions certain functional equations. Concretely, we use that characterizes solve, for arbitrary commutative groups, Ghurye–Olkin’s equation, Wilson’s the Kakutani–Nagumo–Walsh and a general version Fréchet’s unmixed equation.

Generalized Fitzhugh– Nagumo equation; Polynomial differential quadrature method; Numerical solutions; Runge–Kutta method Abstract In this paper, polynomial differential quadrature method (PDQM) is applied to find the numerical solution of the generalized Fitzhugh–Nagumo equation with time-dependent coefficients in one dimensional space. The PDQM reduces the problem into a system of first order...

In this work, q-analogue of the telegraph differential equation is investigated. The approximation solution founded by using Laplace transform collocation method (LTCM). Then, exact compared with for equation. results showed that useful and effective

In this paper we have studied the combination of Elzaki and Laplace transforms to produce a degenerative new double integral transform, transform called Elzaki-Laplace (ELT), then applied it some partial differential equations find its exact solution.