A new numerical approach for solving space–time fractional Schrödinger differential equations via fractional-order Chelyshkov functions
In this paper, a numerical method for solving space–time fractional Schrödinger equations is proposed. The method employs fractional-order Chelyshkov functions and their properties to derive the remainders associated with the main problem. The Riemann–Liouville fractional integral operator is applie...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2025-05-01
|
| Series: | Results in Applied Mathematics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2590037425000482 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849387514604814336 |
|---|---|
| author | Somayeh Nemati Salameh Sedaghat Sajedeh Arefi |
| author_facet | Somayeh Nemati Salameh Sedaghat Sajedeh Arefi |
| author_sort | Somayeh Nemati |
| collection | DOAJ |
| description | In this paper, a numerical method for solving space–time fractional Schrödinger equations is proposed. The method employs fractional-order Chelyshkov functions and their properties to derive the remainders associated with the main problem. The Riemann–Liouville fractional integral operator is applied to the basis functions, yielding exact results through the analytical representation of Chelyshkov polynomials. The real and imaginary parts of the functions involved in the problem are separated, transforming the Schrödinger equation into two equations. By approximating the fractional derivative of the unknown function and using a set of collocation points, the problem is reduced to a system of algebraic equations, the solution of which provides the numerical solution to the problem. Additionally, an error analysis is presented. Finally, numerical examples and their results demonstrate the efficiency and accuracy of the proposed scheme. |
| format | Article |
| id | doaj-art-e1f8a033a0ad41599543602d79c9b46e |
| institution | Kabale University |
| issn | 2590-0374 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Applied Mathematics |
| spelling | doaj-art-e1f8a033a0ad41599543602d79c9b46e2025-08-20T03:53:47ZengElsevierResults in Applied Mathematics2590-03742025-05-012610058410.1016/j.rinam.2025.100584A new numerical approach for solving space–time fractional Schrödinger differential equations via fractional-order Chelyshkov functionsSomayeh Nemati0Salameh Sedaghat1Sajedeh Arefi2Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran; Corresponding author.Department of Mathematics, Buein Zahra Technical University, Buein Zahra, Qazvin, IranDepartment of Applied Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, IranIn this paper, a numerical method for solving space–time fractional Schrödinger equations is proposed. The method employs fractional-order Chelyshkov functions and their properties to derive the remainders associated with the main problem. The Riemann–Liouville fractional integral operator is applied to the basis functions, yielding exact results through the analytical representation of Chelyshkov polynomials. The real and imaginary parts of the functions involved in the problem are separated, transforming the Schrödinger equation into two equations. By approximating the fractional derivative of the unknown function and using a set of collocation points, the problem is reduced to a system of algebraic equations, the solution of which provides the numerical solution to the problem. Additionally, an error analysis is presented. Finally, numerical examples and their results demonstrate the efficiency and accuracy of the proposed scheme.http://www.sciencedirect.com/science/article/pii/S2590037425000482Space–time fractional Schrödinger equationsFractional-order Chelyshkov functionsCaputo derivativeRiemann–Liouville integralError analysis |
| spellingShingle | Somayeh Nemati Salameh Sedaghat Sajedeh Arefi A new numerical approach for solving space–time fractional Schrödinger differential equations via fractional-order Chelyshkov functions Results in Applied Mathematics Space–time fractional Schrödinger equations Fractional-order Chelyshkov functions Caputo derivative Riemann–Liouville integral Error analysis |
| title | A new numerical approach for solving space–time fractional Schrödinger differential equations via fractional-order Chelyshkov functions |
| title_full | A new numerical approach for solving space–time fractional Schrödinger differential equations via fractional-order Chelyshkov functions |
| title_fullStr | A new numerical approach for solving space–time fractional Schrödinger differential equations via fractional-order Chelyshkov functions |
| title_full_unstemmed | A new numerical approach for solving space–time fractional Schrödinger differential equations via fractional-order Chelyshkov functions |
| title_short | A new numerical approach for solving space–time fractional Schrödinger differential equations via fractional-order Chelyshkov functions |
| title_sort | new numerical approach for solving space time fractional schrodinger differential equations via fractional order chelyshkov functions |
| topic | Space–time fractional Schrödinger equations Fractional-order Chelyshkov functions Caputo derivative Riemann–Liouville integral Error analysis |
| url | http://www.sciencedirect.com/science/article/pii/S2590037425000482 |
| work_keys_str_mv | AT somayehnemati anewnumericalapproachforsolvingspacetimefractionalschrodingerdifferentialequationsviafractionalorderchelyshkovfunctions AT salamehsedaghat anewnumericalapproachforsolvingspacetimefractionalschrodingerdifferentialequationsviafractionalorderchelyshkovfunctions AT sajedeharefi anewnumericalapproachforsolvingspacetimefractionalschrodingerdifferentialequationsviafractionalorderchelyshkovfunctions AT somayehnemati newnumericalapproachforsolvingspacetimefractionalschrodingerdifferentialequationsviafractionalorderchelyshkovfunctions AT salamehsedaghat newnumericalapproachforsolvingspacetimefractionalschrodingerdifferentialequationsviafractionalorderchelyshkovfunctions AT sajedeharefi newnumericalapproachforsolvingspacetimefractionalschrodingerdifferentialequationsviafractionalorderchelyshkovfunctions |