fractional differential equation, caputo fractional derivative, caputo-fabrizio fractional derivative, khalouta transform, homotopy per- turbation method, Applied mathematics. Quantitative methods, T57-57.97

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.