a computational method for numerical solution of a nonlinear volterra and fredholm integro-differentialequations of fractional order based on chebyshev cardinal functions is introduced. the chebyshev cardinaloperational matrix of fractional derivative is derived and used to transform the main equation to a system ofalgebraic equations. some examples are included to demonstrate the validity and ...

The modified decomposition method has been implemented for solving a coupled Klein-Gordon Schrödinger equation. We consider a system of coupled Klein-Gordon Schrödinger equation with appropriate initial values using the modified decomposition method. The method does not need linearization, weak nonlinearity assumptions or perturbation theory. The numerical solutions of coupled Klein-Gordon Schr...

<p style='text-indent:20px;'>We consider a damped Klein-Gordon equation with variable diffusion coefficient. This problem is challenging because of the equation's unbounded nonlinearity. First, we study nonlinearity's continuity properties. Then existence and uniqueness solutions established. The main result solution map on set admissible parameters. Its application to parameter identific...

An equation describing particles with spin 3/2 is derived. This equation can be considered as " square root " of the Proca equation in the same sense as the Dirac equation is related to the Klein-Gordon-Fock equation. The equation considered involves fields with spin-3/2 and spin-1/2 (one copy), i.e. multi-spin 1/2, 3/2. The projection operators extracting states with definite energy, spin, and...

In this paper, we find the exact solutions of some nonlinear evolution equations by using ( ′ G )expansion method. Four nonlinear models of physical significance i.e. the symmetric regularized longwave equation, the Klein-Gordon-Zakharov equations, the Burgers-Kadomtsev-Petviashvili equation and the nonlinear Schrödinger equation with a cubic nonlinearity are considered and obtained their exact...

In this paper we consider the nonexistence of global solutions of a Klein-Gordon equation of the form utt −∆u+mu = f(u), (t, x) ∈ [0, T )× Rn. Here m = 0 and the nonlinear power f(u) satisfies some assumptions which will be stated later. We give a sufficient condition on the initial datum with arbitrarily high initial energy such that the solution of the above Klein-Gordon equation blows up in ...