The homotopy analysis method for q-difference equations

Abstract

The q-difference equations are kind of important problems in q-calculus and applied mathematics. In this paper, the homotopy analysis method is extended to find approximate solution for some of q-differential equations. The q-diffusion equation and some examples are analytically investigated. The series solutions obtained by the proposed method are checked by reducing the solutions of q-calculus problems to h-calculus approximate solutions when q→1. Keywords: Quantum calculus, q-difference equations, q-derivative, Homotopy analysis method