Approximate Solution of Time-Fractional Kawahara Equation Using the RBF Collocation Technique

Bahar Karaman; Emrah Karaman; Yılmaz Dereli

doi:10.54974/fcmathsci.1872022

Approximate Solution of Time-Fractional Kawahara Equation Using the RBF Collocation Technique

Abstract

The paper presents an approximate solution to the time-fractional Kawahara equation (TFKE), marking a significant advancement in the field. We decisively utilize the Liouville-Caputo fractional derivative (FD) as the foundation of our analytical framework. To discretize the equations in time, we expertly implement the Crank-Nicolson difference scheme, which guarantees precision and effectiveness. Additionally, we conduct a comprehensive stability analysis of the present scheme, applying the von-Neumann approach designed explicitly for fractional equations. The findings from the numerical experiments are clearly illustrated in the figures, effectively showcasing the robustness and reliability of our approach.

Keywords

Supporting Institution

This paper is supported by Eskişehir Technical University Research Fund under Contract No. 23ADP045.

Project Number

23ADP045

References

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Details

Primary Language

English

Subjects

Numerical Solution of Differential and Integral Equations, Numerical and Computational Mathematics (Other)

Journal Section

Research Article

Authors

Bahar Karaman ^*
0000-0001-6631-8562
Türkiye

Emrah Karaman
0000-0002-0466-3827
Türkiye

Yılmaz Dereli
0000-0003-0149-0542
Türkiye

Publication Date

July 31, 2026

Submission Date

January 26, 2026

Acceptance Date

July 6, 2026

Published in Issue

Year 2026 Volume: 7 Number: 2

DOI

https://doi.org/10.54974/fcmathsci.1872022

IZ

https://izlik.org/JA95JS92NR

Cite

RIS / Bibtex

APA

Karaman, B., Karaman, E., & Dereli, Y. (2026). Approximate Solution of Time-Fractional Kawahara Equation Using the RBF Collocation Technique. Fundamentals of Contemporary Mathematical Sciences, 7(2), 169-184. https://doi.org/10.54974/fcmathsci.1872022

AMA

1.Karaman B, Karaman E, Dereli Y. Approximate Solution of Time-Fractional Kawahara Equation Using the RBF Collocation Technique. FCMS. 2026;7(2):169-184. doi:10.54974/fcmathsci.1872022

Chicago

Karaman, Bahar, Emrah Karaman, and Yılmaz Dereli. 2026. “Approximate Solution of Time-Fractional Kawahara Equation Using the RBF Collocation Technique”. Fundamentals of Contemporary Mathematical Sciences 7 (2): 169-84. https://doi.org/10.54974/fcmathsci.1872022.

EndNote

Karaman B, Karaman E, Dereli Y (July 1, 2026) Approximate Solution of Time-Fractional Kawahara Equation Using the RBF Collocation Technique. Fundamentals of Contemporary Mathematical Sciences 7 2 169–184.

IEEE

[1]B. Karaman, E. Karaman, and Y. Dereli, “Approximate Solution of Time-Fractional Kawahara Equation Using the RBF Collocation Technique”, FCMS, vol. 7, no. 2, pp. 169–184, July 2026, doi: 10.54974/fcmathsci.1872022.

ISNAD

Karaman, Bahar - Karaman, Emrah - Dereli, Yılmaz. “Approximate Solution of Time-Fractional Kawahara Equation Using the RBF Collocation Technique”. Fundamentals of Contemporary Mathematical Sciences 7/2 (July 1, 2026): 169-184. https://doi.org/10.54974/fcmathsci.1872022.

JAMA

1.Karaman B, Karaman E, Dereli Y. Approximate Solution of Time-Fractional Kawahara Equation Using the RBF Collocation Technique. FCMS. 2026;7:169–184.

MLA

Karaman, Bahar, et al. “Approximate Solution of Time-Fractional Kawahara Equation Using the RBF Collocation Technique”. Fundamentals of Contemporary Mathematical Sciences, vol. 7, no. 2, July 2026, pp. 169-84, doi:10.54974/fcmathsci.1872022.

Vancouver

1.Bahar Karaman, Emrah Karaman, Yılmaz Dereli. Approximate Solution of Time-Fractional Kawahara Equation Using the RBF Collocation Technique. FCMS. 2026 Jul. 1;7(2):169-84. doi:10.54974/fcmathsci.1872022