Solutions of the Fractional Combined KdV-mKdV Equation Using the Special Generalized Hyperbolic and Trigonometric Functions

Sevil Çulha Ünal

doi:10.54187/jnrs.1619374

EN

Solutions of the Fractional Combined KdV-mKdV Equation Using the Special Generalized Hyperbolic and Trigonometric Functions

Abstract

The combined KdV-mKdV equation is one of the essential equations used in soliton physics. In this study, the analytical solutions of the space-time fractional combined KdV-mKdV equation are gained using the Sardar sub-equation approach. In this equation, the fractional derivatives are given in a conformable sense. A clue on how we can convert the fractional partial differential equation into an ordinary differential equation to acquire analytical solutions is presented in this paper. The acquired solutions are obtained in special generalized hyperbolic and trigonometric forms. The different types of soliton solutions are also found. Some are illustrated by selecting the appropriate parameter values in 2D and 3D graphs. Finally, the suggested approach is reliable, effective, and beneficial for solving many nonlinear integer and fractional order differential equations.

Keywords

Combined KdV-mKdV equation, special generalized hyperbolic and trigonometric functions, conformable fractional derivative, soliton solutions, traveling wave solutions

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Details

Primary Language

English

Subjects

Mathematical Methods and Special Functions

Journal Section

Research Article

Authors

Sevil Çulha Ünal ^*
0000-0001-7447-9219
Türkiye

Publication Date

April 30, 2025

Submission Date

January 13, 2025

Acceptance Date

April 15, 2025

Published in Issue

Year 2025 Volume: 14 Number: 1

DOI

https://doi.org/10.54187/jnrs.1619374

IZ

https://izlik.org/JA33NW54BP

APA

Çulha Ünal, S. (2025). Solutions of the Fractional Combined KdV-mKdV Equation Using the Special Generalized Hyperbolic and Trigonometric Functions. Journal of New Results in Science, 14(1), 1-13. https://doi.org/10.54187/jnrs.1619374

AMA

1.Çulha Ünal S. Solutions of the Fractional Combined KdV-mKdV Equation Using the Special Generalized Hyperbolic and Trigonometric Functions. JNRS. 2025;14(1):1-13. doi:10.54187/jnrs.1619374

Chicago

Çulha Ünal, Sevil. 2025. “Solutions of the Fractional Combined KdV-MKdV Equation Using the Special Generalized Hyperbolic and Trigonometric Functions”. Journal of New Results in Science 14 (1): 1-13. https://doi.org/10.54187/jnrs.1619374.

EndNote

Çulha Ünal S (April 1, 2025) Solutions of the Fractional Combined KdV-mKdV Equation Using the Special Generalized Hyperbolic and Trigonometric Functions. Journal of New Results in Science 14 1 1–13.

IEEE

[1]S. Çulha Ünal, “Solutions of the Fractional Combined KdV-mKdV Equation Using the Special Generalized Hyperbolic and Trigonometric Functions”, JNRS, vol. 14, no. 1, pp. 1–13, Apr. 2025, doi: 10.54187/jnrs.1619374.

ISNAD

Çulha Ünal, Sevil. “Solutions of the Fractional Combined KdV-MKdV Equation Using the Special Generalized Hyperbolic and Trigonometric Functions”. Journal of New Results in Science 14/1 (April 1, 2025): 1-13. https://doi.org/10.54187/jnrs.1619374.

JAMA

1.Çulha Ünal S. Solutions of the Fractional Combined KdV-mKdV Equation Using the Special Generalized Hyperbolic and Trigonometric Functions. JNRS. 2025;14:1–13.

MLA

Çulha Ünal, Sevil. “Solutions of the Fractional Combined KdV-MKdV Equation Using the Special Generalized Hyperbolic and Trigonometric Functions”. Journal of New Results in Science, vol. 14, no. 1, Apr. 2025, pp. 1-13, doi:10.54187/jnrs.1619374.

Vancouver

1.Sevil Çulha Ünal. Solutions of the Fractional Combined KdV-mKdV Equation Using the Special Generalized Hyperbolic and Trigonometric Functions. JNRS. 2025 Apr. 1;14(1):1-13. doi:10.54187/jnrs.1619374