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

Year 2025, Volume: 14 Issue: 1, 1 - 13, 30.04.2025

Sevil Çulha Ünal

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

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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