Extension of the Optimal Auxiliary Function Method to Solve the System of a Fractional-Order Whitham–Broer–Kaup Equation

• Published in: Fractal and fractional Vol. 8; no. 1; p. 1
• Main Authors: Alsheekhhussain, Zainab, Moaddy, Khaled, Shah, Rasool, Alshammari, Saleh, Alshammari, Mohammad, Al-Sawalha, M. Mossa, Alderremy, Aisha Abdullah
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.01.2024
• Subjects: Approximation; Calculus; Caputo operator; Complex systems; Differential equations; Engineering; Entropy; fractional-order Whitham–Broer–Kaup equation; Methods; Nonlinear differential equations; Nonlinear equations; Numerical analysis; optimal auxiliary function method; Partial differential equations; Physics
• ISSN: 2504-3110; 2504-3110
• DOI: 10.3390/fractalfract8010001

In this paper, we introduce and implement the optimal auxiliary function method to solve a system of fractional-order Whitham–Broer–Kaup equations, a class of nonlinear partial differential equations with broad applications in mathematical physics. This method provides a systematic and efficient approach to finding accurate solutions for complex systems of fractional-order equations. We give a full analysis using tables and figures to demonstrate the reliability and accuracy of our approach. We confirm the effectiveness of our suggested method in solving the considered equations using numerical simulations and comparisons, emphasizing its potential for applications in a variety of scientific and engineering areas.