An Application of Incomplete I-Functions with Two Variables to Solve the Nonlinear Differential Equations Using S-Function

Abstract

In this article, we evaluate the approximate solutions of Nonlinear Differential Equations (NoLDEs) with the association of S-function, incomplete H-functions (IHFs) and incomplete I-functions (IIFs) with two variables by using the Hermite, Legendre and Jacobi polynomials. Here, we introduce incomplete I-functions with two variables. The NoLDEs are significantly applicable in fluid dynamics, vibration problems, population dynamics, electromagnetism, chemical kinetics, combustion theory, economics and finance. Recently, it was implemented to solve the resistance less circuit with a nonlinear capacitor under influence of external periodic force. This method is established as an application of improper integrals, polynomials and special functions. The obtained results are helpful to get the
solution of various problems of mathematical physics and engineering in approximate aspects