Reliable analysis for time-fractional nonlinear differential difference equations

In this study, we used HPM to determine the approximate analytical solution of nonlinear differential difference equations of fractional time derivative. By using initial conditions, the explicit solutions of the coupled nonlinear differential difference equations have been derived which demonstrate the effectiveness, potentiality and validity of the method in reality. The present method is very effective and powerful to determine the solution of system of non-linear DDE. The numerical calculations are carried out when the initial condition in the form of hyperbolic functions and the results are shown through the graphs.