The series solution is widely applied to differential equations onR but is not found in q-differential equations. Applying the Taylor andmultiplication rule of two generalized polynomials, we develop a series solution of linear homogeneous q-difference equations. As an example, the series solution method is used to find a series solution of the second-order q-difference equation of Hermite’s type.

This article investigates different nonlinear systems of fractional partial differential equations analytically using an attractive modified method known as the Laplace residual power series technique. Based on a combination transformation and technique, we achieve analytic approximation results in rapid convergent form by employing notion limit, with less time effort than method. Three challen...