Novel Dynamic Behaviors in Fractional Chaotic Systems: Numerical Simulations with Caputo Derivatives
Over the last several years, there has been a considerable improvement in the possible methods for solving fractional-order chaotic systems; however, achieving high accuracy remains a challenge. This work proposes a new precise numerical technique for fractional-order chaotic systems. Through simula...
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2024-11-01
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| author | Mohamed A. Abdoon Diaa Eldin Elgezouli Borhen Halouani Amr M. Y. Abdelaty Ibrahim S. Elshazly Praveen Ailawalia Alaa H. El-Qadeem |
| author_facet | Mohamed A. Abdoon Diaa Eldin Elgezouli Borhen Halouani Amr M. Y. Abdelaty Ibrahim S. Elshazly Praveen Ailawalia Alaa H. El-Qadeem |
| author_sort | Mohamed A. Abdoon |
| collection | DOAJ |
| description | Over the last several years, there has been a considerable improvement in the possible methods for solving fractional-order chaotic systems; however, achieving high accuracy remains a challenge. This work proposes a new precise numerical technique for fractional-order chaotic systems. Through simulations, we obtain new types of complex and previously undiscussed dynamic behaviors.These phenomena, not recognized in prior numerical results or theoretical estimations, underscore the unique dynamics present in fractional systems. We also study the effects of the fractional parameters <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>β</mi><mn>1</mn></msub></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>β</mi><mn>2</mn></msub></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>β</mi><mn>3</mn></msub></semantics></math></inline-formula> on the system’s behavior, comparing them to integer-order derivatives. It has been demonstrated via the findings that the suggested technique is consistent with conventional numerical methods for integer-order systems while simultaneously providing an even higher level of precision. It is possible to demonstrate the efficacy and precision of this technique through simulations, which demonstrates that this method is useful for the investigation of complicated chaotic models. |
| format | Article |
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| institution | Kabale University |
| issn | 2075-1680 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj-art-b75dd1302e0c423f96e9e12ee8a4fb842024-11-26T17:50:55ZengMDPI AGAxioms2075-16802024-11-01131179110.3390/axioms13110791Novel Dynamic Behaviors in Fractional Chaotic Systems: Numerical Simulations with Caputo DerivativesMohamed A. Abdoon0Diaa Eldin Elgezouli1Borhen Halouani2Amr M. Y. Abdelaty3Ibrahim S. Elshazly4Praveen Ailawalia5Alaa H. El-Qadeem6Department of Basic Sciences, Common First Year Deanship, King Saud University, P.O. Box 1142, Riyadh 12373, 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 Basic Sciences, Common First Year Deanship, King Saud University, P.O. Box 1142, Riyadh 12373, Saudi ArabiaDepartment of Basic Sciences, Common First Year Deanship, King Saud University, P.O. Box 1142, Riyadh 12373, Saudi ArabiaDepartment of Mathematics, University Institute of Sciences, Chandigarh University, Gharaun, Mohali 140403, Punjab, IndiaDepartment of Mathematics, Faculty of Science, Zagazig University, Zagazig 44519, EgyptOver the last several years, there has been a considerable improvement in the possible methods for solving fractional-order chaotic systems; however, achieving high accuracy remains a challenge. This work proposes a new precise numerical technique for fractional-order chaotic systems. Through simulations, we obtain new types of complex and previously undiscussed dynamic behaviors.These phenomena, not recognized in prior numerical results or theoretical estimations, underscore the unique dynamics present in fractional systems. We also study the effects of the fractional parameters <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>β</mi><mn>1</mn></msub></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>β</mi><mn>2</mn></msub></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>β</mi><mn>3</mn></msub></semantics></math></inline-formula> on the system’s behavior, comparing them to integer-order derivatives. It has been demonstrated via the findings that the suggested technique is consistent with conventional numerical methods for integer-order systems while simultaneously providing an even higher level of precision. It is possible to demonstrate the efficacy and precision of this technique through simulations, which demonstrates that this method is useful for the investigation of complicated chaotic models.https://www.mdpi.com/2075-1680/13/11/791complex dynamic behaviorfractional derivativeshigh-precisionsimulationchaos |
| spellingShingle | Mohamed A. Abdoon Diaa Eldin Elgezouli Borhen Halouani Amr M. Y. Abdelaty Ibrahim S. Elshazly Praveen Ailawalia Alaa H. El-Qadeem Novel Dynamic Behaviors in Fractional Chaotic Systems: Numerical Simulations with Caputo Derivatives Axioms complex dynamic behavior fractional derivatives high-precision simulation chaos |
| title | Novel Dynamic Behaviors in Fractional Chaotic Systems: Numerical Simulations with Caputo Derivatives |
| title_full | Novel Dynamic Behaviors in Fractional Chaotic Systems: Numerical Simulations with Caputo Derivatives |
| title_fullStr | Novel Dynamic Behaviors in Fractional Chaotic Systems: Numerical Simulations with Caputo Derivatives |
| title_full_unstemmed | Novel Dynamic Behaviors in Fractional Chaotic Systems: Numerical Simulations with Caputo Derivatives |
| title_short | Novel Dynamic Behaviors in Fractional Chaotic Systems: Numerical Simulations with Caputo Derivatives |
| title_sort | novel dynamic behaviors in fractional chaotic systems numerical simulations with caputo derivatives |
| topic | complex dynamic behavior fractional derivatives high-precision simulation chaos |
| url | https://www.mdpi.com/2075-1680/13/11/791 |
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