A comparative analysis of k-Katugampola and generalized Atangana–Baleanu fractional derivatives for solving the fractional Zakharov–Kuznetsov equation in dusty plasma

Articles in Press

Document Type : Research Article

Authors

Elyas Shivanian ¹

Amanullah Nabavi ²

Mohammad Ali Zirak ³

Abbas Poya ³

Hedayat Fatahi ⁴

¹ Department of Applied Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, 34149-16818, Iran.

² Department of Mathematics, Natural faculty, Bamyan University, Bamyan, Afghanistan.

³ Department of Mathematics,Daykondi University, Nili, Afghanistan.

⁴ Department of Mathematics, Sanandaj Branch, Islamic Azad University, Baneh, Iran.

10.22067/ijnao.2026.96269.1769

Abstract

In this paper, both linear and nonlinear higher-dimensional equations—such as the fractional-order Zakharov–Kuznetsov equation, a model widely used in physics and mathematics to describe ion-acoustic dust waves in magnetized plasmas with two ion temperatures—are comparatively investigated using the generalized variational iteration method, by employing the k-Katugampola fractional derivative and the generalized Atangana–Baleanu derivative, which allow for a simple and effective solution of differential equations A comparative study is conducted using the k-Katugampola and generalized Zakharov–Kuznetsov Atangana–Baleanu fractional derivatives to solve higher-dimensional linear and nonlinear differential equations. The fractional-order Zakharov–Kuznetsov equation, which models ion-acoustic dust waves in magnetized plasmas with two ion temperatures, is investigated using the generalized variational iteration method. The existence and uniqueness of the solution to the equation are established, along with the convergence of the proposed method. Numerical simulations—including 2D and 3D plots and absolute error analysis for various fractional and integer orders—confirm the efficiency and accuracy of the proposed approach using MATLAB software.

Keywords

(k)-Katugampula fractional derivative

Generalized Atangan-Baleanu fractional derivative

Zakharov&ndash

Kuznetsov fractional-order equation

Reconstruction of variational iteration method

Subjects

• Computational Mathematics

---