Abstract
In this paper, we find the approximate solution of a nonlinear differential equations pertaining to M-series, H over bar -function, and I-function of two variables by making use of the Hermite, Legendre, and Jacobi polynomials. The nonlinear differential equations play a key role in distinct branches of engineering and physics and many vibration problems. The results obtained in the present study are general in nature and can be used to obtain the solution of various problems of physics and engineering.