Analytical Approximate Solution of Conformable Fractional Fifth-Order Korteweg-de Vries Equation via the ARA-residual Power Series Method

Abstract

In this paper, we introduce an analytical method for deriving an approximate solution to the time-dependent fifth-order Korteweg-de Vries (fKdV) equation using the conformable fractional derivative (CFD) via the ARA-residual power series method (ARA-RPSM). The proposed method operates by initially applying the ARA-transform to the given fKdV equation. Subsequently, approximate series solutions are derived using Taylor’s expansion. These series solutions are then converted back into the original domain through the inverse ARA-transform. It is a general method for time-dependent nonlinear differential equations and has wide applicability. The efficiency and flexibility of this method make it useful for a wide range of time-dependent nonlinear differential equations. To demonstrate its effectiveness, we apply it to the time-dependent fKdV equation, showcasing how it generates reliable and accurate series solutions quickly.