On theoretical and numerical analysis of Time-Fractional Fornberg-Whitham Equation

Jassim, Hassan Kamil; Yasser, Mohammed Taimah

doi:10.22034/cmde.2025.65002.2966

On theoretical and numerical analysis of Time-Fractional Fornberg-Whitham Equation

Articles in Press

Document Type : Research Paper

Authors

¹ Department of Mathematics, Faculty of Education for Pure Sciences, University of Thi-Qar, Iraq.

² Department of Mathematics, Faculty of Education, Al-Ayen Iraqi University, Thi-Qar, Iraq.

10.22034/cmde.2025.65002.2966

Abstract

In this study, the Atangana-Baleanu fractional operator was employed with
the Fornberg-Witham equation to investigate The computational solutions to this
equation. The existence and uniqueness of the solution were proven using precise
mathematical conditions that ensure their validity. Furthermore, the convergence
of the approximated solutions derived through the use of the Yang-Daftardar-Jafari
Method (YDJM) to the exact solutions was verified. The effectiveness of the proposed
method was tested by applying it to two illustrative examples. The results
demonstrated that the solutions obtained through this method exhibit high accuracy
and align well with the analytical solutions under certain conditions, which
highlights the efficiency of the method in handling nonlinear fractional differential
equations.

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Main Subjects