Using Laplace Residual Power Series Method in Solving Coupled Fractional Neutron Diffusion Equations with Delayed Neutrons System
In this paper, a system of coupled fractional neutron diffusion equations with delayed neutrons was solved efficiently by using a combination of residual power series and Laplace transform techniques, and the anomalous diffusion was considered by taking the non-Gaussian case with different values of...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-02-01
|
| Series: | Fractal and Fractional |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/7/3/219 |
| _version_ | 1797611689602973696 |
|---|---|
| author | Mohammed Shqair Ibrahim Ghabar Aliaa Burqan |
| author_facet | Mohammed Shqair Ibrahim Ghabar Aliaa Burqan |
| author_sort | Mohammed Shqair |
| collection | DOAJ |
| description | In this paper, a system of coupled fractional neutron diffusion equations with delayed neutrons was solved efficiently by using a combination of residual power series and Laplace transform techniques, and the anomalous diffusion was considered by taking the non-Gaussian case with different values of fractional parameter α. The Laplace residual power series method (LRPSM) does not require differentiation, conversion, or discretization for the assumed conditions, so the approach is simple and suitable for solving higher-order fractional differential equations. To assure the theoretical results, two different neutron flux initial conditions were presented numerically, where the needed Mathematica codes were performed using essential nuclear reactor cross-section data, and the results for different values of times were tabulated and graphically figured out. Finally, it must be noted that the results align with the Adomian decomposition method. |
| first_indexed | 2024-03-11T06:31:20Z |
| format | Article |
| id | doaj.art-b7727c075d2a476db68bef9a17b3e9b0 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-11T06:31:20Z |
| publishDate | 2023-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-b7727c075d2a476db68bef9a17b3e9b02023-11-17T11:11:59ZengMDPI AGFractal and Fractional2504-31102023-02-017321910.3390/fractalfract7030219Using Laplace Residual Power Series Method in Solving Coupled Fractional Neutron Diffusion Equations with Delayed Neutrons SystemMohammed Shqair0Ibrahim Ghabar1Aliaa Burqan2College of Science, Zarqa University, Zarqa 13110, JordanCollege of Science, Zarqa University, Zarqa 13110, JordanCollege of Science, Zarqa University, Zarqa 13110, JordanIn this paper, a system of coupled fractional neutron diffusion equations with delayed neutrons was solved efficiently by using a combination of residual power series and Laplace transform techniques, and the anomalous diffusion was considered by taking the non-Gaussian case with different values of fractional parameter α. The Laplace residual power series method (LRPSM) does not require differentiation, conversion, or discretization for the assumed conditions, so the approach is simple and suitable for solving higher-order fractional differential equations. To assure the theoretical results, two different neutron flux initial conditions were presented numerically, where the needed Mathematica codes were performed using essential nuclear reactor cross-section data, and the results for different values of times were tabulated and graphically figured out. Finally, it must be noted that the results align with the Adomian decomposition method.https://www.mdpi.com/2504-3110/7/3/219diffusion equationkinetic point equationLaplace residual power seriesfractional calculus |
| spellingShingle | Mohammed Shqair Ibrahim Ghabar Aliaa Burqan Using Laplace Residual Power Series Method in Solving Coupled Fractional Neutron Diffusion Equations with Delayed Neutrons System Fractal and Fractional diffusion equation kinetic point equation Laplace residual power series fractional calculus |
| title | Using Laplace Residual Power Series Method in Solving Coupled Fractional Neutron Diffusion Equations with Delayed Neutrons System |
| title_full | Using Laplace Residual Power Series Method in Solving Coupled Fractional Neutron Diffusion Equations with Delayed Neutrons System |
| title_fullStr | Using Laplace Residual Power Series Method in Solving Coupled Fractional Neutron Diffusion Equations with Delayed Neutrons System |
| title_full_unstemmed | Using Laplace Residual Power Series Method in Solving Coupled Fractional Neutron Diffusion Equations with Delayed Neutrons System |
| title_short | Using Laplace Residual Power Series Method in Solving Coupled Fractional Neutron Diffusion Equations with Delayed Neutrons System |
| title_sort | using laplace residual power series method in solving coupled fractional neutron diffusion equations with delayed neutrons system |
| topic | diffusion equation kinetic point equation Laplace residual power series fractional calculus |
| url | https://www.mdpi.com/2504-3110/7/3/219 |
| work_keys_str_mv | AT mohammedshqair usinglaplaceresidualpowerseriesmethodinsolvingcoupledfractionalneutrondiffusionequationswithdelayedneutronssystem AT ibrahimghabar usinglaplaceresidualpowerseriesmethodinsolvingcoupledfractionalneutrondiffusionequationswithdelayedneutronssystem AT aliaaburqan usinglaplaceresidualpowerseriesmethodinsolvingcoupledfractionalneutrondiffusionequationswithdelayedneutronssystem |