A numerical approach for multi-dimensional ψ-Hilfer fractional nonlinear Galilei invariant advection–diffusion equations
In this paper, we introduce the ψ-Hilfer fractional version of nonlinear Galilei-invariant advection–diffusion equations in one and two dimensions. A new type of basic functions, namely the ψ-Chebyshev cardinal functions (CFs), is introduced to establish a hybrid numerical strategy to solve these eq...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2025-01-01
|
| Series: | Results in Physics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2211379724007526 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832595727274999808 |
|---|---|
| author | M.H. Heydari M. Razzaghi M. Bayram |
| author_facet | M.H. Heydari M. Razzaghi M. Bayram |
| author_sort | M.H. Heydari |
| collection | DOAJ |
| description | In this paper, we introduce the ψ-Hilfer fractional version of nonlinear Galilei-invariant advection–diffusion equations in one and two dimensions. A new type of basic functions, namely the ψ-Chebyshev cardinal functions (CFs), is introduced to establish a hybrid numerical strategy to solve these equations. The key advantageous property of these functions is the simplicity of computing their ψ-Hilfer fractional derivative. Utilizing this property, a new operational matrix for the ψ-Hilfer fractional derivative of these functions is derived. Consequently, a hybrid numerical strategy based on the shifted Chebyshev polynomials (CPs) and ψ-Chebyshev CFs is proposed to solve these equations. More precisely, in the proposed strategy, a finite expansion for the solution of the equation under investigation is considered. The shifted CPs are used to approximate the solution in the spatial domain, while the ψ-Chebyshev CFs are utilized to approximate the solution in the temporal domain. By applying the ψ-Hilfer fractional derivative operational matrix of the ψ-Chebyshev CFs, the classical derivatives operational matrices of the shifted CPs, and employing the collocation method, the solution of the equation under consideration is obtained by solving a system whose elements are algebraic equations. The accuracy of the presented strategy is examined by numerous examples. |
| format | Article |
| id | doaj-art-01065e9d9e87469c8b17b85a7e667e74 |
| institution | Kabale University |
| issn | 2211-3797 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Physics |
| spelling | doaj-art-01065e9d9e87469c8b17b85a7e667e742025-01-18T05:04:28ZengElsevierResults in Physics2211-37972025-01-0168108067A numerical approach for multi-dimensional ψ-Hilfer fractional nonlinear Galilei invariant advection–diffusion equationsM.H. Heydari0M. Razzaghi1M. Bayram2Department of Mathematics, Shiraz University of Technology, Shiraz, Iran; Corresponding author.Department of Mathematics and Statistics, Mississippi State University, Mississippi State, MS 39762, USADepartment of Computer Engineering, Biruni University, Istanbul, TurkeyIn this paper, we introduce the ψ-Hilfer fractional version of nonlinear Galilei-invariant advection–diffusion equations in one and two dimensions. A new type of basic functions, namely the ψ-Chebyshev cardinal functions (CFs), is introduced to establish a hybrid numerical strategy to solve these equations. The key advantageous property of these functions is the simplicity of computing their ψ-Hilfer fractional derivative. Utilizing this property, a new operational matrix for the ψ-Hilfer fractional derivative of these functions is derived. Consequently, a hybrid numerical strategy based on the shifted Chebyshev polynomials (CPs) and ψ-Chebyshev CFs is proposed to solve these equations. More precisely, in the proposed strategy, a finite expansion for the solution of the equation under investigation is considered. The shifted CPs are used to approximate the solution in the spatial domain, while the ψ-Chebyshev CFs are utilized to approximate the solution in the temporal domain. By applying the ψ-Hilfer fractional derivative operational matrix of the ψ-Chebyshev CFs, the classical derivatives operational matrices of the shifted CPs, and employing the collocation method, the solution of the equation under consideration is obtained by solving a system whose elements are algebraic equations. The accuracy of the presented strategy is examined by numerous examples.http://www.sciencedirect.com/science/article/pii/S2211379724007526ψ-Hilfer fractionalGalilei invariant advection–diffusion equationsψ-Chebyshev cardinal functionsShifted Chebyshev polynomials |
| spellingShingle | M.H. Heydari M. Razzaghi M. Bayram A numerical approach for multi-dimensional ψ-Hilfer fractional nonlinear Galilei invariant advection–diffusion equations Results in Physics ψ-Hilfer fractional Galilei invariant advection–diffusion equations ψ-Chebyshev cardinal functions Shifted Chebyshev polynomials |
| title | A numerical approach for multi-dimensional ψ-Hilfer fractional nonlinear Galilei invariant advection–diffusion equations |
| title_full | A numerical approach for multi-dimensional ψ-Hilfer fractional nonlinear Galilei invariant advection–diffusion equations |
| title_fullStr | A numerical approach for multi-dimensional ψ-Hilfer fractional nonlinear Galilei invariant advection–diffusion equations |
| title_full_unstemmed | A numerical approach for multi-dimensional ψ-Hilfer fractional nonlinear Galilei invariant advection–diffusion equations |
| title_short | A numerical approach for multi-dimensional ψ-Hilfer fractional nonlinear Galilei invariant advection–diffusion equations |
| title_sort | numerical approach for multi dimensional ψ hilfer fractional nonlinear galilei invariant advection diffusion equations |
| topic | ψ-Hilfer fractional Galilei invariant advection–diffusion equations ψ-Chebyshev cardinal functions Shifted Chebyshev polynomials |
| url | http://www.sciencedirect.com/science/article/pii/S2211379724007526 |
| work_keys_str_mv | AT mhheydari anumericalapproachformultidimensionalpshilferfractionalnonlineargalileiinvariantadvectiondiffusionequations AT mrazzaghi anumericalapproachformultidimensionalpshilferfractionalnonlineargalileiinvariantadvectiondiffusionequations AT mbayram anumericalapproachformultidimensionalpshilferfractionalnonlineargalileiinvariantadvectiondiffusionequations AT mhheydari numericalapproachformultidimensionalpshilferfractionalnonlineargalileiinvariantadvectiondiffusionequations AT mrazzaghi numericalapproachformultidimensionalpshilferfractionalnonlineargalileiinvariantadvectiondiffusionequations AT mbayram numericalapproachformultidimensionalpshilferfractionalnonlineargalileiinvariantadvectiondiffusionequations |