Analytical and numerical study on the solutions of a new (2+1)-dimensional conformable shallow water wave equation

Mehmet Şenol; Furkan Muzaffer Çelik

Makale detayları

Analytical and numerical study on the solutions of a new (2+1)-dimensional conformable shallow water wave equation

Yazarlar:

Mehmet Şenol | Furkan Muzaffer Çelik

Yayıncı:

Ankara University

Ana Başlıklar:

Mathematical Methods and Special Functions

Dergi:

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics Vol.74 Issue 1, pp.1-16

Belge Tipi:

Makale

Yayın Tarihi:

8/2025

Belge Dili:

İngilizce

Document ID (Org No.):

2001341516

pISSN:

1303-5991

Anahtar kelimeler:

Özet:

 The 21-dimensional conformable nonlinear shallow water wave equation is examined in this work. Initially, definitions and properties of suitable derivatives are presented. Subsequently, exact solutions to this equation are derived using the expϕξ-expansion and the modified extended tanh function methods. Then, a numerical method, namely the residual power series method, is utilized to obtain approximate solutions. The interplay between analytical and numerical approaches is explored to validate the solutions. This study fills a gap in the literature on fractional shallow water models, particularly in 21 dimensions, and offers new insights into wave dynamics governed by fractional derivatives. The physical implications of the findings are illustrated through 3D and 2D contour surfaces of some obtained data, offering insight into the physical interpretation of geometric structures. A table is also presented to compare the obtained results. These solutions highlight the practical uses of the investigated model and other nonlinear models in applied sciences. These techniques can potentially yield significant results in solving various fractional differential equations.

 The 21-dimensional conformable nonlinear shallow water wave equation is examined in this work. Initially, definitions and properties of suitable derivatives are presented. Subsequently, exact solutions to this equation are derived using the expϕξ-expansion and the modified extended tanh function methods. Then, a numerical method, namely the residual power series method, is utilized to obtain approximate solutions. The interplay between analytical and numerical approaches is explored to validate the solutions. This study fills a gap in the literature on fractional shallow water models, particularly in 21 dimensions, and offers new insights into wave dynamics governed by fractional derivatives. The physical implications of the findings are illustrated through 3D and 2D contour surfaces of some obtained data, offering insight into the physical interpretation of geometric structures. A table is also presented to compare the obtained results. These solutions highlight the practical uses of the investigated model and other nonlinear models in applied sciences. These techniques can potentially yield significant results in solving various fractional differential equations.

 The 21-dimensional conformable nonlinear shallow water wave equation is examined in this work. Initially, definitions and properties of suitable derivatives are presented. Subsequently, exact solutions to this equation are derived using the expϕξ-expansion and the modified extended tanh function methods. Then, a numerical method, namely the residual power series method, is utilized to obtain approximate solutions. The interplay between analytical and numerical approaches is explored to validate the solutions. This study fills a gap in the literature on fractional shallow water models, particularly in 21 dimensions, and offers new insights into wave dynamics governed by fractional derivatives. The physical implications of the findings are illustrated through 3D and 2D contour surfaces of some obtained data, offering insight into the physical interpretation of geometric structures. A table is also presented to compare the obtained results. These solutions highlight the practical uses of the investigated model and other nonlinear models in applied sciences. These techniques can potentially yield significant results in solving various fractional differential equations.

 The 21-dimensional conformable nonlinear shallow water wave equation is examined in this work. Initially, definitions and properties of suitable derivatives are presented. Subsequently, exact solutions to this equation are derived using the expϕξ-expansion and the modified extended tanh function methods. Then, a numerical method, namely the residual power series method, is utilized to obtain approximate solutions. The interplay between analytical and numerical approaches is explored to validate the solutions. This study fills a gap in the literature on fractional shallow water models, particularly in 21 dimensions, and offers new insights into wave dynamics governed by fractional derivatives. The physical implications of the findings are illustrated through 3D and 2D contour surfaces of some obtained data, offering insight into the physical interpretation of geometric structures. A table is also presented to compare the obtained results. These solutions highlight the practical uses of the investigated model and other nonlinear models in applied sciences. These techniques can potentially yield significant results in solving various fractional differential equations.

Makale detayları

Analytical and numerical study on the solutions of a new (2+1)-dimensional conformable shallow water wave equation

Yazarlar:

Mehmet Şenol | Furkan Muzaffer Çelik

Yayıncı:

Ankara University

Ana Başlıklar:

Mathematical Methods and Special Functions

Dergi:

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics Vol.74 Issue 1, pp.1-16

Belge Tipi:

Makale

Yayın Tarihi:

8/2025

Belge Dili:

İngilizce

Document ID (Org No.):

2001341516

pISSN:

1303-5991

The exp(–φ(ξ))-expansion method

modified extended tanh-function method

residual power series method

shallow water wave equation

conformable derivative

Sayı

Makale detayları

Analytical and numerical study on the solutions of a new (2+1)-dimensional conformable shallow water wave equation

Yazarlar: Mehmet Şenol | Furkan Muzaffer Çelik

Yayıncı: Ankara University

Ana Başlıklar: Mathematical Methods and Special Functions

Dergi: Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics Vol.74 Issue 1, pp.1-16

Belge Tipi: Makale

Yayın Tarihi: 8/2025

Belge Dili: İngilizce

Document ID (Org No.): 2001341516

pISSN: 1303-5991

The exp(–φ(ξ))-expansion method

modified extended tanh-function method

residual power series method

shallow water wave equation

conformable derivative

Sayı

Yazarlar:

Mehmet Şenol | Furkan Muzaffer Çelik

Yayıncı:

Ankara University

Ana Başlıklar:

Mathematical Methods and Special Functions

Dergi:

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics Vol.74 Issue 1, pp.1-16

Belge Tipi:

Makale

Yayın Tarihi:

8/2025

Belge Dili:

İngilizce

Document ID (Org No.):

2001341516

pISSN:

1303-5991