The Fractional Investigation of Some Nonlinear Partial Differential Equations by Using an Efficient Procedure

The nonlinearity inmany problems occurs because of the complexity of the given physical phenomena. The present paper investigates the non-linear fractional partial differential equations' solutions using the Caputo operator with Laplace residual power seriesmethod. It is found that the present technique has a direct and simple implementation to solve the targeted problems. The comparison of the obtained solutions has been done with actual solutions to the problems. The fractional-order solutions are presented and considered to be the focal point of this research article. The results of the proposed technique are highly accurate and provide useful information about the actual dynamics of each problem. Because of the simple implementation, the present technique can be extended to solve other important fractional order problems.

Automated summary

The present paper investigates the solutions of non-linear fractional partial differential equations using the Caputo operator with Laplace residual power series method. The technique is found to have a direct and simple implementation and the obtained solutions are highly accurate. The focus of this research article is the fractional-order solutions, which provide useful information about the actual dynamics of each problem. The present technique can be extended to solve other important fractional order problems due to its simplicity.