On the Solution of Mathematical Model Including Space-Time Fractional Diffusion Equation in Conformable Derivative, Via Weighted Inner Product

Süleyman Çetinkaya; Ali Demir

Makale detayları

On the Solution of Mathematical Model Including Space-Time Fractional Diffusion Equation in Conformable Derivative, Via Weighted Inner Product

Yazarlar:

Süleyman Çetinkaya | Ali Demir

Yayıncı:

Kocaeli University

Ana Başlıklar:

Uygulamalı Matematik

Dergi:

Kocaeli Journal of Science and Engineering Vol.6 Issue 1, pp.1-6

Belge Tipi:

Makale

Yayın Tarihi:

5/2023

Belge Dili:

İngilizce

Document ID (Org No.):

2001290336

pISSN:

2667-484X

Anahtar kelimeler:

Özet:

 This research aims to accomplish an analytic solution to mathematical models involving space-time fractional differential equations in the conformable sense in series form through the weighted inner product and separation of variables method. The main advantage of this method is that various linear problems of any kind of differential equations can be solved by using this method. First, the corresponding eigenfunctions are established by solving the Sturm-Liouville eigenvalue problem. Secondly, the coefficients of the eigenfunctions are determined by employing weighted inner product and initial condition. Thirdly, the analytic solution to the problem is constructed in the series form. Finally, an illustrative example is presented to show how this method is implemented for fractional problems and exhibit its effectiveness and accuracy.

 This research aims to accomplish an analytic solution to mathematical models involving space-time fractional differential equations in the conformable sense in series form through the weighted inner product and separation of variables method. The main advantage of this method is that various linear problems of any kind of differential equations can be solved by using this method. First, the corresponding eigenfunctions are established by solving the Sturm-Liouville eigenvalue problem. Secondly, the coefficients of the eigenfunctions are determined by employing weighted inner product and initial condition. Thirdly, the analytic solution to the problem is constructed in the series form. Finally, an illustrative example is presented to show how this method is implemented for fractional problems and exhibit its effectiveness and accuracy.

 This research aims to accomplish an analytic solution to mathematical models involving space-time fractional differential equations in the conformable sense in series form through the weighted inner product and separation of variables method. The main advantage of this method is that various linear problems of any kind of differential equations can be solved by using this method. First, the corresponding eigenfunctions are established by solving the Sturm-Liouville eigenvalue problem. Secondly, the coefficients of the eigenfunctions are determined by employing weighted inner product and initial condition. Thirdly, the analytic solution to the problem is constructed in the series form. Finally, an illustrative example is presented to show how this method is implemented for fractional problems and exhibit its effectiveness and accuracy.

 This research aims to accomplish an analytic solution to mathematical models involving space-time fractional differential equations in the conformable sense in series form through the weighted inner product and separation of variables method. The main advantage of this method is that various linear problems of any kind of differential equations can be solved by using this method. First, the corresponding eigenfunctions are established by solving the Sturm-Liouville eigenvalue problem. Secondly, the coefficients of the eigenfunctions are determined by employing weighted inner product and initial condition. Thirdly, the analytic solution to the problem is constructed in the series form. Finally, an illustrative example is presented to show how this method is implemented for fractional problems and exhibit its effectiveness and accuracy.

Makale detayları

On the Solution of Mathematical Model Including Space-Time Fractional Diffusion Equation in Conformable Derivative, Via Weighted Inner Product

Yazarlar:

Süleyman Çetinkaya | Ali Demir

Yayıncı:

Kocaeli University

Ana Başlıklar:

Uygulamalı Matematik

Dergi:

Kocaeli Journal of Science and Engineering Vol.6 Issue 1, pp.1-6

Belge Tipi:

Makale

Yayın Tarihi:

5/2023

Belge Dili:

İngilizce

Document ID (Org No.):

2001290336

pISSN:

2667-484X

Conformable fractional derivative

Initial-boundary-value problems

Space-time fractional differential equation

Spectral method

Sayı

Makale detayları

On the Solution of Mathematical Model Including Space-Time Fractional Diffusion Equation in Conformable Derivative, Via Weighted Inner Product

Yazarlar: Süleyman Çetinkaya | Ali Demir

Yayıncı: Kocaeli University

Ana Başlıklar: Uygulamalı Matematik

Dergi: Kocaeli Journal of Science and Engineering Vol.6 Issue 1, pp.1-6

Belge Tipi: Makale

Yayın Tarihi: 5/2023

Belge Dili: İngilizce

Document ID (Org No.): 2001290336

pISSN: 2667-484X

Conformable fractional derivative

Initial-boundary-value problems

Space-time fractional differential equation

Spectral method

Sayı

Yazarlar:

Süleyman Çetinkaya | Ali Demir

Yayıncı:

Kocaeli University

Ana Başlıklar:

Uygulamalı Matematik

Dergi:

Kocaeli Journal of Science and Engineering Vol.6 Issue 1, pp.1-6

Belge Tipi:

Makale

Yayın Tarihi:

5/2023

Belge Dili:

İngilizce

Document ID (Org No.):

2001290336

pISSN:

2667-484X