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

Articles in Press

Document Type : Research Article

Author

• Ali 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 fractional Khalouta homotopy 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 presented. To evaluate the effectiveness of the proposed computational strategy, we examine the convergence of the series solution over different fractional values alpha and evaluate the behavior of the solution as the time domain increases. The efficiency and originality of the FKHHPM are demonstrated by calculating the absolute error. This work is supported by two-dimensional and three-dimensional graphical representations made in accordance with MATLAB.

Keywords

• Fractional differential equation
• Caputo fractional derivative
• Caputo-Fabrizio fractional derivative
• Khalouta transform
• homotopy perturbation method

Main Subjects

• Numerical methods for differential equations and its applications

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