In this article, we present the modified generalized Mittag-Leffler function method (MGMLFM) as an approximate- analytical method to give a proper solution of time-fractional Korteweg-de Vries (KdV) and Korteweg-de Vries-Burger’s (KdVB) equations, which have various applications in physics and applied mathematics. The time-fractional partial derivatives are based on Caputo sense. The obtained solution is constructed in a rapidly convergent power series. By comparing the approximate MGMLFM solutions when the fractional operator equal one with known exact solutions we have an appropriate agreement. The advantage of the article is to apply the suggested method to solve linear and nonlinear time-fractional partial differential equations, where it needs less computational effort which saves time and effort. The convergence of absolute error be controlled on by the parameters in the time- fractional KdV and KdVB equations were found. The simulation of the obtained results is presented in the forms of graphs to illustrate the reliability and efficiency of our method.
Mohamed Ali, Hegagi
"An efficient approximate-analytical method to solve time-fractional KdV and KdVB equations,"
Information Sciences Letters: Vol. 9
, Article 10.
Available at: https://digitalcommons.aaru.edu.jo/isl/vol9/iss3/10