Analytical Approach for the Approximate Solution of Harry Dym Equation with Caputo Fractional Derivative

This paper presents the concept of a new strategy that examines the analytical solution of the Harry Dym equation (HDEq) with fractional derivative in the Caputo sense. This new approach is called the Mohand homotopy perturbation transform scheme (MHPTS) which is constructed on the basis of the Mohand transform (MT) and the homotopy perturbation method (HPM). The implementation of MT produces the recurrence relation without any assumption and hypothesis theory whereas HPM is additionally used to overcome the nonlinearity in differential problems. Our primary focus is to handle the error analysis in the recurrence relation and generates the solution in the order of series. These obtained results yield the exact solution very rapidly due to its fast convergence. Some graphical representations are demonstrated to show the high efficiency and performance of this approach.

Automated summary

This paper presents a new strategy, called the Mohand homotopy perturbation transform scheme (MHPTS), to analyze the analytical solution of the Harry Dym equation with fractional derivative. The MHPTS combines the Mohand transform and the homotopy perturbation method to handle the error analysis in the recurrence relation and achieve fast convergence for generating exact solutions.