Discrete Homotopy Analysis Method to Solve Nabla Fractional Partial Difference Equations

Abstract

In the present work, the discrete homotopy analysis method is applied to solve nabla time-fractional
partial difference equations. Fractional difference operator is considered in Caputo’s sense. We apply the
discrete homotopy analysis method to nabla fractional initial value problems. Obtained solutions involve
an auxiliary parameter h, which we can determine. Thus, it may be concluded that the discrete homotopy
analysis method is a very powerful and successful analytical approach for fractional difference equations.