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

Document Type : Research Article

Author

• A. Khalouta

Laboratory of Fundamental and Numerical Mathematics, Department of Mathematics, Faculty of Sciences, Setif 1 University-Ferhat ABBAS, Algeria.

10.22067/ijnao.2025.89967.1523

Abstract

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.

Keywords

• Fractional differential equation
• Caputo fractional derivative
• Caputo-Fabrizio fractional derivative
• Khalouta transform
• Homotopy per- turbation method

Main Subjects

• Numerical methods for differential equations and its applications

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