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

Sevil Çulha Ünal

Makale detayları

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

Yazarlar:

Sevil Çulha Ünal

Yayıncı:

Tokat Gaziosmanpasa University

Ana Başlıklar:

Mathematical Methods and Special Functions

Dergi:

Journal of New Results in Science Vol.14 Issue 1, pp.1-13

Belge Tipi:

Makale

Yayın Tarihi:

4/2025

Belge Dili:

İngilizce

Document ID (Org No.):

2001347471

pISSN:

1304-7981

Anahtar kelimeler:

Özet:

 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.

 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.

 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.

 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.

Makale detayları

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

Yazarlar:

Sevil Çulha Ünal

Yayıncı:

Tokat Gaziosmanpasa University

Ana Başlıklar:

Mathematical Methods and Special Functions

Dergi:

Journal of New Results in Science Vol.14 Issue 1, pp.1-13

Belge Tipi:

Makale

Yayın Tarihi:

4/2025

Belge Dili:

İngilizce

Document ID (Org No.):

2001347471

pISSN:

1304-7981

Combined KdV-mKdV equation

special generalized hyperbolic and trigonometric functions

conformable fractional derivative

soliton solutions

traveling wave solutions

Sayı

Makale detayları

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

Yazarlar: Sevil Çulha Ünal

Yayıncı: Tokat Gaziosmanpasa University

Ana Başlıklar: Mathematical Methods and Special Functions

Dergi: Journal of New Results in Science Vol.14 Issue 1, pp.1-13

Belge Tipi: Makale

Yayın Tarihi: 4/2025

Belge Dili: İngilizce

Document ID (Org No.): 2001347471

pISSN: 1304-7981

Combined KdV-mKdV equation

special generalized hyperbolic and trigonometric functions

conformable fractional derivative

soliton solutions

traveling wave solutions

Sayı

Yazarlar:

Sevil Çulha Ünal

Yayıncı:

Tokat Gaziosmanpasa University

Ana Başlıklar:

Mathematical Methods and Special Functions

Dergi:

Journal of New Results in Science Vol.14 Issue 1, pp.1-13

Belge Tipi:

Makale

Yayın Tarihi:

4/2025

Belge Dili:

İngilizce

Document ID (Org No.):

2001347471

pISSN:

1304-7981