On the Construction of The Laplace Transform via Gamma Function

Ufuk Kaya; Şeyda Ermiş

Makale detayları

On the Construction of The Laplace Transform via Gamma Function

Yazarlar:

Ufuk Kaya | Şeyda Ermiş

Yayıncı:

Bitlis Eren University

Ana Başlıklar:

Ordinary Differential Equations | Difference Equations and Dynamical Systems

Dergi:

Bitlis Eren Üniversitesi Fen Bilimleri Dergisi Vol.13 Issue 4, pp.1247-1259

Belge Tipi:

Makale

Yayın Tarihi:

12/2024

Belge Dili:

İngilizce

Document ID (Org No.):

2001336496

pISSN:

2147-3129

Anahtar kelimeler:

Özet:

 The Laplace transform can be applied to integrable and exponential-type functions on the half-line 0, by the formula Lf_0fx e-sx dx. This transform reduces differential equations to algebraic equations and solves many non-homogeneous differential equations. However, the Laplace transform cannot be applied to some functions such as x- 94, because the given integral is divergent. So, the Laplace transform do not solve some differential equations with some terms such as x- 94. This transform needs a revision to include such functions to solve a wider class of differential equations. In this study, we defined the Ω-Laplace transform, which eliminates such insufficiency of the Laplace transform and is a generalization of it. We applied this new operator to previously unsolved differential equations and obtained solutions. Ω-Laplace ensform given with the help of series: fx_n0c_n xr_n  Ωf_n0c_n Γr_n1sr_n1 Moreover, we give the similar and different properties of this transform to the Laplace transform.

 The Laplace transform can be applied to integrable and exponential-type functions on the half-line 0, by the formula Lf_0fx e-sx dx. This transform reduces differential equations to algebraic equations and solves many non-homogeneous differential equations. However, the Laplace transform cannot be applied to some functions such as x- 94, because the given integral is divergent. So, the Laplace transform do not solve some differential equations with some terms such as x- 94. This transform needs a revision to include such functions to solve a wider class of differential equations. In this study, we defined the Ω-Laplace transform, which eliminates such insufficiency of the Laplace transform and is a generalization of it. We applied this new operator to previously unsolved differential equations and obtained solutions. Ω-Laplace ensform given with the help of series: fx_n0c_n xr_n  Ωf_n0c_n Γr_n1sr_n1 Moreover, we give the similar and different properties of this transform to the Laplace transform.

 The Laplace transform can be applied to integrable and exponential-type functions on the half-line 0, by the formula Lf_0fx e-sx dx. This transform reduces differential equations to algebraic equations and solves many non-homogeneous differential equations. However, the Laplace transform cannot be applied to some functions such as x- 94, because the given integral is divergent. So, the Laplace transform do not solve some differential equations with some terms such as x- 94. This transform needs a revision to include such functions to solve a wider class of differential equations. In this study, we defined the Ω-Laplace transform, which eliminates such insufficiency of the Laplace transform and is a generalization of it. We applied this new operator to previously unsolved differential equations and obtained solutions. Ω-Laplace ensform given with the help of series: fx_n0c_n xr_n  Ωf_n0c_n Γr_n1sr_n1 Moreover, we give the similar and different properties of this transform to the Laplace transform.

 The Laplace transform can be applied to integrable and exponential-type functions on the half-line 0, by the formula Lf_0fx e-sx dx. This transform reduces differential equations to algebraic equations and solves many non-homogeneous differential equations. However, the Laplace transform cannot be applied to some functions such as x- 94, because the given integral is divergent. So, the Laplace transform do not solve some differential equations with some terms such as x- 94. This transform needs a revision to include such functions to solve a wider class of differential equations. In this study, we defined the Ω-Laplace transform, which eliminates such insufficiency of the Laplace transform and is a generalization of it. We applied this new operator to previously unsolved differential equations and obtained solutions. Ω-Laplace ensform given with the help of series: fx_n0c_n xr_n  Ωf_n0c_n Γr_n1sr_n1 Moreover, we give the similar and different properties of this transform to the Laplace transform.

Makale detayları

On the Construction of The Laplace Transform via Gamma Function

Yazarlar:

Ufuk Kaya | Şeyda Ermiş

Yayıncı:

Bitlis Eren University

Ana Başlıklar:

Ordinary Differential Equations | Difference Equations and Dynamical Systems

Dergi:

Bitlis Eren Üniversitesi Fen Bilimleri Dergisi Vol.13 Issue 4, pp.1247-1259

Belge Tipi:

Makale

Yayın Tarihi:

12/2024

Belge Dili:

İngilizce

Document ID (Org No.):

2001336496

pISSN:

2147-3129

Differential equations

Laplace Transform

Operators

Gamma function

Series

Sayı

Makale detayları

On the Construction of The Laplace Transform via Gamma Function

Yazarlar: Ufuk Kaya | Şeyda Ermiş

Yayıncı: Bitlis Eren University

Ana Başlıklar: Ordinary Differential Equations | Difference Equations and Dynamical Systems

Dergi: Bitlis Eren Üniversitesi Fen Bilimleri Dergisi Vol.13 Issue 4, pp.1247-1259

Belge Tipi: Makale

Yayın Tarihi: 12/2024

Belge Dili: İngilizce

Document ID (Org No.): 2001336496

pISSN: 2147-3129

Differential equations

Laplace Transform

Operators

Gamma function

Series

Sayı

Yazarlar:

Ufuk Kaya | Şeyda Ermiş

Yayıncı:

Bitlis Eren University

Ana Başlıklar:

Ordinary Differential Equations | Difference Equations and Dynamical Systems

Dergi:

Bitlis Eren Üniversitesi Fen Bilimleri Dergisi Vol.13 Issue 4, pp.1247-1259

Belge Tipi:

Makale

Yayın Tarihi:

12/2024

Belge Dili:

İngilizce

Document ID (Org No.):

2001336496

pISSN:

2147-3129