Application of Analytical Techniques for Solving Fractional Physical Models Arising in Applied Sciences

In this paper, we examined the approximations to the time-fractional Kawahara equation and modified Kawahara equation, which model the creation of nonlinear water waves in the long wavelength area and the transmission of signals. We implemented two novel techniques, namely the homotopy perturbation transform method and the Elzaki transform decomposition method. The derivative having fractional-order is taken in Caputo sense. The Adomian and He's polynomials make it simple to handle the nonlinear terms. To illustrate the adaptability and effectiveness of derivatives with fractional order to represent the water waves in long wavelength regions, numerical data have been given graphically. A key component of the Kawahara equation is the symmetry pattern, and the symmetrical nature of the solution may be observed in the graphs. The importance of our suggested methods is illustrated by the convergence of analytical solutions to the precise solutions. The techniques currently in use are straightforward and effective for solving fractional-order issues. The offered methods reduced computational time is their main advantage. It will be possible to solve fractional partial differential equations using the study's findings as a tool.

Automated summary

In this paper, we examined the approximations to the time-fractional Kawahara equation and modified Kawahara equation using two novel techniques, the homotopy perturbation transform method and the Elzaki transform decomposition method. The adaptability and effectiveness of derivatives with fractional order to represent water waves in long wavelength regions were demonstrated through numerical data. The importance of the suggested methods was illustrated by the convergence of analytical solutions to the precise solutions, and their main advantage is the reduced computational time.