Efficient Computational Approach for Generalized Fractional KdV–Burgers Equation

Abstract

A collocation method based on double summations of Mittag–Leffler functions is proposed to solve the Korteweg–de Vries (KdV) and Burgers equation of fractional order with initial-boundary conditions. The resulting algebraic system is constructed as a constrained optimization problem and optimized to obtain the unknown coefficients. Error analysis of the approximation solution is studied. Simulations of the results are studied graphically through representations for the effect of fractional order parameters and time levels. The results ensure that the proposed method is accurate and efficient.