New numerical simulation for fractional Benney-Lin equation arising in falling film problems using two novel techniques

The pivotal aim of the present work is to find the numerical solution for fractional Benney-Lin equation by using two efficient methods, calledq-homotopy analysis transform method and fractional natural decomposition method. The considered equation exemplifies the long waves on the liquid films. Projected methods are distinct with solution procedure and they are modified with different transform algorithms. To illustrate the reliability and applicability of the considered solution procedures we consider eight special cases with different initial conditions. The fractional operator is considered in Caputo sense. The achieved results are drowned through two and three-dimensional plots for different Brownian motions and classical order. The numerical simulations are presented to ensure the efficiency of considered techniques. The behavior of the obtained results for distinct fractional order is captured in the present framework. The outcomes of the present investigation show that, the considered schemes are efficient and powerful to solve nonlinear differential equations arise in science and technology.

Automated summary

The study aims to find the numerical solution for the fractional Benney-Lin equation using the q-homotopy analysis transform method and fractional natural decomposition method, modified with different transform algorithms. By considering eight special cases with different initial conditions, the reliability and applicability of the proposed solution procedures are illustrated, showing efficiency in solving nonlinear differential equations in science and technology.