an accurate numerical technique for solving a special case of fractional differential equations using the khalouta transform of two different fractional derivatives

The aim of this paper is to present a novel coupling approach of the khalouta transform method and the homotopy perturbation method in order to obtain an accurate and efficient method for solving a special case of fractional differential equations involving caputo and caputo-fabrizio fractional derivatives. this method is called the fractional khalouta ho-motopy perturbation method (fkhhpm). in particular, the fkhhpm is used to obtain a solution to the fractional reaction-diffusion-convection equations. the convergence analysis and a numerical example are pre-sented. to evaluate the effectiveness of the proposed computational strat-egy, we examine the convergence of the series solution over different frac-tional values and evaluate the behavior of the solution as the time do-main increases. the efficiency and originality of the fkhhpm are demon-strated by calculating the absolute error. this work is supported by two-dimensional and three-dimensional graphical representations made in ac-cordance with matlab.