The q-difference equations are important in q-calculus. In this paper, we apply the iterative method which is suggested by Daftardar and Jafari, hereafter called the Daftardar-Jafari method, for solving a type of q-partial differential equations. We discuss the convergency of this method. In the implementation of this technique according to other iterative methods such as Adomian decomposition and homotopy perturbation methods, one does not need the calculation of the Adomian’s polynomials for nonlinear terms. It is proven that under a special constraint, the given result by this method converges to exact solution of nonlinear q-ordinary or q-partial differential equations.
Jafari, Hossein; Jane Johnston, Sarah; Mahmood Sani, Sajad; and Baleanu, Dumitru
"A Decomposition Method for Solving q-Difference Equations,"
Applied Mathematics & Information Sciences: Vol. 09
, Article 18.
Available at: https://dc.naturalspublishing.com/amis/vol09/iss6/18