On Comparing Analytical and Numerical Solutions of Time Caputo Fractional Kawahara Equations via Some Techniques

One of the important techniques for solving several partial differential equations is the residual power series method, which provides the approximate solutions of differential equations in power series form.In this work, we use Aboodh transform in the analogical structure of the residual power series method to obtain a new method called the Aboodh residual power series method (ARPSM). By using this technique, we calculate the coefficients of some power series solutions of time Caputo fractional Kawahara equations. To obtain analytical and numerical solutions for the TCFKEs, we use ARPSM, first with the approximate initial condition and then with the exact initial condition. We present ARPSM’s reliability, efficiency, and capability by graphically describing the numerical results for analytical solutions and by comparing our solutions with other solutions for the TCFKEs obtained using two alternative methods, namely, the residual power series method and the natural transform decomposition method.