Numerical solution of the conformable fractional diffusion equation

In this paper, a numerical approach for solving space-time fractional diffusion equation with variable coefficients is proposed. The fractional derivatives are described in the conformable sense. The numerical approach is based on shifted Chebyshev polynomials of the second kind. The space-time frac...

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Published inMathematical notes (Miskolci Egyetem (Hungary)) Vol. 23; no. 2; pp. 975 - 986
Main Author Yaslan, H. Cerdik
Format Journal Article
LanguageEnglish
Published Miskolc University of Miskolc 2022
Subjects
Chebyshev approximation
Differential equations
Diffusion
Finite difference method
Polynomials
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ISSN1787-2405
1787-2413
DOI10.18514/MMN.2022.3669

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Abstract In this paper, a numerical approach for solving space-time fractional diffusion equation with variable coefficients is proposed. The fractional derivatives are described in the conformable sense. The numerical approach is based on shifted Chebyshev polynomials of the second kind. The space-time fractional diffusion equation with variable coefficients is reduced to a system of ordinary differential equations by using the properties of Chebyshev polynomials. The finite difference method is applied to solve this system of equations. Numerical results are provided to verify the accuracy and efficiency of the proposed approach.
AbstractList In this paper, a numerical approach for solving space-time fractional diffusion equation with variable coefficients is proposed. The fractional derivatives are described in the conformable sense. The numerical approach is based on shifted Chebyshev polynomials of the second kind. The space-time fractional diffusion equation with variable coefficients is reduced to a system of ordinary differential equations by using the properties of Çhebyshev polynomials. The finite difference method is applied to solve this system of equations. Numerical results are provided to verify the accuracy and efficiency of the proposed approach.
In this paper, a numerical approach for solving space-time fractional diffusion equation with variable coefficients is proposed. The fractional derivatives are described in the conformable sense. The numerical approach is based on shifted Chebyshev polynomials of the second kind. The space-time fractional diffusion equation with variable coefficients is reduced to a system of ordinary differential equations by using the properties of Chebyshev polynomials. The finite difference method is applied to solve this system of equations. Numerical results are provided to verify the accuracy and efficiency of the proposed approach.
Author Yaslan, H. Cerdik
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Snippet In this paper, a numerical approach for solving space-time fractional diffusion equation with variable coefficients is proposed. The fractional derivatives are...
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SubjectTerms Chebyshev approximation
Differential equations
Diffusion
Finite difference method
Polynomials
Title Numerical solution of the conformable fractional diffusion equation
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