In this article, a hybrid method that combines Aboodh transform, variational iteration method, and the homotopyperturbation is presented for approximate solution of important partial differential equations describe wave like in one, two three dimensions. The suggested utilizes only initial conditions to providean analytical solution, contrast separation variables, also requires boundary conditi...

Using the ranks and Moore-Penrose inverses of involved matrices, in this paper we establish some necessary sufficient solvability conditions for a system Sylvester-type quaternion matrix equations, give an expression general solution to when it is solvable. As application system, consider special symmetry solution, named η-Hermitian equations. Moreover, present algorithm numerical example verif...