A Comparative Study and Numerical Solutions for the Fractional Modified Lorenz–Stenflo System Using Two Methods
This paper provides a solution to the new fractional-order Lorenz–Stenflo model using the adaptive predictor–corrector approach and the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ρ</mi></semant...
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2024-12-01
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| author | Mohamed Elbadri Mohamed A. Abdoon Abdulrahman B. M. Alzahrani Rania Saadeh Mohammed Berir |
| author_facet | Mohamed Elbadri Mohamed A. Abdoon Abdulrahman B. M. Alzahrani Rania Saadeh Mohammed Berir |
| author_sort | Mohamed Elbadri |
| collection | DOAJ |
| description | This paper provides a solution to the new fractional-order Lorenz–Stenflo model using the adaptive predictor–corrector approach and the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ρ</mi></semantics></math></inline-formula>-Laplace New Iterative Method (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>L</mi><mi>ρ</mi></msub><mi>N</mi><mi>I</mi><mi>M</mi></mrow></semantics></math></inline-formula>), representing an extensive comparison between both techniques with RK4 related to accuracy and error analysis. The results show that the suggested approaches allow one to be more accurate in analyzing the dynamics of the system. These techniques also produce results that are comparable to the results of other approximate techniques. The techniques can, thus, be used on a wider class of systems in order to provide more accurate results. These techniques also appropriately identify chaotic attractors in the system. These techniques can be applied to solve various numerical problems arising in science and engineering in the future. |
| format | Article |
| id | doaj-art-8e48058c6ef04bfc94c2ce769429d28e |
| institution | Kabale University |
| issn | 2075-1680 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj-art-8e48058c6ef04bfc94c2ce769429d28e2025-01-24T13:22:10ZengMDPI AGAxioms2075-16802024-12-011412010.3390/axioms14010020A Comparative Study and Numerical Solutions for the Fractional Modified Lorenz–Stenflo System Using Two MethodsMohamed Elbadri0Mohamed A. Abdoon1Abdulrahman B. M. Alzahrani2Rania Saadeh3Mohammed Berir4Mathematics Department, College of Science, Jouf University, Sakaka 72388, Saudi ArabiaDepartment of Basic Sciences, Common First Year Deanship, King Saud University, P.O. Box 1142, Riyadh 12373, Saudi ArabiaDepartment of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi ArabiaDepartment of Mathematics, Zarqa University, Zarqa 13110, JordanDepartment of Mathematics, Faculty of Science and Arts, Al-Baha University, Al-Baha 61008, Saudi ArabiaThis paper provides a solution to the new fractional-order Lorenz–Stenflo model using the adaptive predictor–corrector approach and the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ρ</mi></semantics></math></inline-formula>-Laplace New Iterative Method (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>L</mi><mi>ρ</mi></msub><mi>N</mi><mi>I</mi><mi>M</mi></mrow></semantics></math></inline-formula>), representing an extensive comparison between both techniques with RK4 related to accuracy and error analysis. The results show that the suggested approaches allow one to be more accurate in analyzing the dynamics of the system. These techniques also produce results that are comparable to the results of other approximate techniques. The techniques can, thus, be used on a wider class of systems in order to provide more accurate results. These techniques also appropriately identify chaotic attractors in the system. These techniques can be applied to solve various numerical problems arising in science and engineering in the future.https://www.mdpi.com/2075-1680/14/1/20new iterative <i>ρ</i>-Laplace methodAPC-G methodfractional derivativessimulationchaos |
| spellingShingle | Mohamed Elbadri Mohamed A. Abdoon Abdulrahman B. M. Alzahrani Rania Saadeh Mohammed Berir A Comparative Study and Numerical Solutions for the Fractional Modified Lorenz–Stenflo System Using Two Methods Axioms new iterative <i>ρ</i>-Laplace method APC-G method fractional derivatives simulation chaos |
| title | A Comparative Study and Numerical Solutions for the Fractional Modified Lorenz–Stenflo System Using Two Methods |
| title_full | A Comparative Study and Numerical Solutions for the Fractional Modified Lorenz–Stenflo System Using Two Methods |
| title_fullStr | A Comparative Study and Numerical Solutions for the Fractional Modified Lorenz–Stenflo System Using Two Methods |
| title_full_unstemmed | A Comparative Study and Numerical Solutions for the Fractional Modified Lorenz–Stenflo System Using Two Methods |
| title_short | A Comparative Study and Numerical Solutions for the Fractional Modified Lorenz–Stenflo System Using Two Methods |
| title_sort | comparative study and numerical solutions for the fractional modified lorenz stenflo system using two methods |
| topic | new iterative <i>ρ</i>-Laplace method APC-G method fractional derivatives simulation chaos |
| url | https://www.mdpi.com/2075-1680/14/1/20 |
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