Solution of local fractional generalized coupled Korteweg–de Vries (cKdV) equation using local fractional homotopy analysis method and Adomian decomposition method

Abstract

In this study, time-fractional coupled Korteweg–de Vries (cKdV) equations are solved using an efficient and reliable numerical technique. The classical cKdV system has been generalized into the time-fractional cKdV system. We employ the local fractional homotopy analysis method (LFHAM) and the Adomian decomposition method (ADM) to propose an approximate solution for fractional cKdV equations. Both approaches determined findings are compared together. The findings clearly demonstrate that the suggested methods are appropriate and efficient for handling both linear and nonlinear issues in engineering and sciences. To demonstrate the suggested approaches' competencies, examples are provided. Convergent series form has been used to make the solutions. The relevance of the techniques is illustrated through graphic representations of the solution.

Keywords

• Local fractional derivative
• coupled Korteweg–de Vries equation
• homotopy analysis method
• Adomian decomposition method
• 34A34
• 65M06