A Comparative Study of the Fractional Partial Differential Equations via Novel Transform

Abstract

In comparison to fractional-order differential equations, integer-order differential equations generally fail to properly explain a variety of phenomena in numerous branches of science and engineering. This article implements efficient analytical techniques within the Caputo operator to investigate the solutions of some fractional partial differential equations. The Adomian decomposition method, homotopy perturbation method, and Elzaki transformation are used to calculate the results for the specified issues. In the current procedures, we first used the Elzaki transform to simplify the problems and then applied the decomposition and perturbation methods to obtain comprehensive results for the problems. For each targeted problem, the generalized schemes of the suggested methods are derived under the influence of each fractional derivative operator. The current approaches give a series-form solution with easily computable components and a higher rate of convergence to the precise solution of the targeted problems. It is observed that the derived solutions have a strong connection to the actual solutions of each problem as the number of terms in the series solution of the problems increases. Graphs in two and three dimensions are used to plot the solution of the proposed fractional models. The methods used currently are simple and efficient for dealing with fractional-order problems. The primary benefit of the suggested methods is less computational time. The results of the current study will be regarded as a helpful tool for dealing with the solution of fractional partial differential equations.