Solution of the non-linear time-fractional Kudryashov–Sinelshchikov equation using fractional reduced differential transform method

In this research, we analyze the non-linear time-fractional Kudryashov–Sinelshchikov equation, which represents waves induced by pressure inside the combination of gas bubbles and liquid, considering heat transfer and viscidness of liquid among gas bubbles and liquid. The non-linear Kudryashov–Sinelshchikov equation having fractional order is numerically solved employing the fractional reduced differential transform method (FRDTM). We have conducted a convergence analysis of the solution series obtained through FRDTM. Also, the FRDTM generates the solution without perturbation, discretization, or linearization. The numerical solution and error analysis of this non-linear Kudryashov–Sinelshchikov equation having fractional order with respect to time using FRDTM completely conforms with the exact solution as shown precisely in 2D and 3D graphs. The results of this research demonstrate the effectiveness and accuracy of the FRDTM in solving the non-linear time-fractional Kudryashov–Sinelshchikov equation.