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-fractionalpartial difference equations. Fractional difference operator is considered in Caputo’s sense. We apply thediscrete homotopy analysis method to nabla fractional initial value problems. Obtained solutions involvean auxiliary parameter h, which we can determine. Thus, it may be concluded that the discrete homotopyanalysis method is a very powerful and successful analytical approach for fractional difference equations.