Investigating the Impact of Fractional Non-Linearity in the Klein–Fock–Gordon Equation on Quantum Dynamics
In this paper, we investigate the fractional-order Klein–Fock–Gordon equations on quantum dynamics using a new iterative method and residual power series method based on the Caputo operator. The fractional-order Klein–Fock–Gordon equation is a generalization of the traditional Klein–Fock–Gordon equa...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-04-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/15/4/881 |
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| author | Saima Noor Azzh Saad Alshehry Noufe H. Aljahdaly Hina M. Dutt Imran Khan Rasool Shah |
| author_facet | Saima Noor Azzh Saad Alshehry Noufe H. Aljahdaly Hina M. Dutt Imran Khan Rasool Shah |
| author_sort | Saima Noor |
| collection | DOAJ |
| description | In this paper, we investigate the fractional-order Klein–Fock–Gordon equations on quantum dynamics using a new iterative method and residual power series method based on the Caputo operator. The fractional-order Klein–Fock–Gordon equation is a generalization of the traditional Klein–Fock–Gordon equation that allows for non-integer orders of differentiation. This equation has been used in the study of quantum dynamics to model the behavior of particles with fractional spin. The Laplace transform is employed to transform the equations into a simpler form, and the resulting equations are then solved using the proposed methods. The accuracy and efficiency of the method are demonstrated through numerical simulations, which show that the method is superior to existing numerical methods in terms of accuracy and computational time. The proposed method is applicable to a wide range of fractional-order differential equations, and it is expected to find applications in various areas of science and engineering. |
| first_indexed | 2024-03-11T04:29:32Z |
| format | Article |
| id | doaj.art-e91d058f2f1143b39ddaef70c14cd0fd |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-11T04:29:32Z |
| publishDate | 2023-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-e91d058f2f1143b39ddaef70c14cd0fd2023-11-17T21:34:04ZengMDPI AGSymmetry2073-89942023-04-0115488110.3390/sym15040881Investigating the Impact of Fractional Non-Linearity in the Klein–Fock–Gordon Equation on Quantum DynamicsSaima Noor0Azzh Saad Alshehry1Noufe H. Aljahdaly2Hina M. Dutt3Imran Khan4Rasool Shah5Department of Basic Sciences, Preparatory Year Deanship, King Faisal University, Al Ahsa 31982, Saudi ArabiaDepartment of Mathematical Sciences, Faculty of Sciences, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi ArabiaDepartment of Mathematics, Faculty of Sciences and Arts, King Abdulaziz University, Rabigh 21911, Saudi ArabiaDepartment of Humanities and Sciences, School of Electrical Engineering and Computer Science (SEECS), National University of Sciences and Technology (NUST), Islamabad 44000, PakistanDepartment of Mathematics, Abdul Wali Khan University, Mardan 23200, PakistanDepartment of Mathematics, Abdul Wali Khan University, Mardan 23200, PakistanIn this paper, we investigate the fractional-order Klein–Fock–Gordon equations on quantum dynamics using a new iterative method and residual power series method based on the Caputo operator. The fractional-order Klein–Fock–Gordon equation is a generalization of the traditional Klein–Fock–Gordon equation that allows for non-integer orders of differentiation. This equation has been used in the study of quantum dynamics to model the behavior of particles with fractional spin. The Laplace transform is employed to transform the equations into a simpler form, and the resulting equations are then solved using the proposed methods. The accuracy and efficiency of the method are demonstrated through numerical simulations, which show that the method is superior to existing numerical methods in terms of accuracy and computational time. The proposed method is applicable to a wide range of fractional-order differential equations, and it is expected to find applications in various areas of science and engineering.https://www.mdpi.com/2073-8994/15/4/881residual power seriesLaplace transformfractional-order Klein–Fock–Gordon equationsnew iterative methodCaputo operator |
| spellingShingle | Saima Noor Azzh Saad Alshehry Noufe H. Aljahdaly Hina M. Dutt Imran Khan Rasool Shah Investigating the Impact of Fractional Non-Linearity in the Klein–Fock–Gordon Equation on Quantum Dynamics Symmetry residual power series Laplace transform fractional-order Klein–Fock–Gordon equations new iterative method Caputo operator |
| title | Investigating the Impact of Fractional Non-Linearity in the Klein–Fock–Gordon Equation on Quantum Dynamics |
| title_full | Investigating the Impact of Fractional Non-Linearity in the Klein–Fock–Gordon Equation on Quantum Dynamics |
| title_fullStr | Investigating the Impact of Fractional Non-Linearity in the Klein–Fock–Gordon Equation on Quantum Dynamics |
| title_full_unstemmed | Investigating the Impact of Fractional Non-Linearity in the Klein–Fock–Gordon Equation on Quantum Dynamics |
| title_short | Investigating the Impact of Fractional Non-Linearity in the Klein–Fock–Gordon Equation on Quantum Dynamics |
| title_sort | investigating the impact of fractional non linearity in the klein fock gordon equation on quantum dynamics |
| topic | residual power series Laplace transform fractional-order Klein–Fock–Gordon equations new iterative method Caputo operator |
| url | https://www.mdpi.com/2073-8994/15/4/881 |
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