Fractional order systems: an overview of mathematics, design, and applications for engineers
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| Format: | Book |
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| Language: | English |
| Published: |
Amsterdam
Academic Press
2021
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| Series: | Emerging methodologies and applications in modelling, identification and control
1 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xiii, 598 Seiten Illustratienen, Diagramme 23 cm |
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Record in the Search Index
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| adam_text | Contents List of contributors 1. A survey on numerical studies for fractional biological models and their optima) control ХІ 1 N.H. Sweilam and S.M. AL-Mekhlafi 1.1. 1.2. Introduction Primary definitions of fractional calculus 1 2 1.3. 1.4. Fractional optimal control problem A survey on fractional biological models and their optimal control 3 4 1.5. 1.6. A survey on numerical methods for solving fractional optimal control biological models A novel fractional-order malaria mathematical model 7 13 1.7. 1.8. HFOCP Numerical experiment and discussion 16 25 1.9. Conclusions 26 References 2. A collection of interdisciplinary applications of fractional-order circuits 30 35 Panagiotis Berisiąs, Stavroula Kapoulea, Costas Psychalinos, and Ahmed S. Elwakil 3. 2.1. 2.2. Introduction Implementation of the approximated Laplacian operator 35 36 2.3. 2.4. Biomedical signal processing applications Bio-impedance applications 41 51 2.5. Sensor applications 2.6. Conclusions and discussion Acknowledgments 63 66 67 References 67 Fractional-order control 71 Ivo Petráš 3.1. Introduction 3.2. 3.3. 3.4. Fractional-order systems and controllers New fractional-order control techniques Discussion and conclusions Acknowledgment References 71 73 81 101 103 103 v
Contents VI 4. Fractional-order systems, numerical techniques, and applications 107 Fawang Liu, Pinghui Zhuang, Qingxia Liu, Minling Zheng, and Vo V. Anh 4.1. introduction 107 4.2. Numerical methods for solving the multiterm time-fractional diffusion-wave equation 112 4.3. Analytical solution of the multiterm time-fractional differential equation and application to unsteady flow of generalized viscoelastic fluid 121 4.4. Numerical analysis of multiterm time-fractional viscoelastic nonNewtonian fluid models for simulating unsteady MHD Couette flow of generalized Oldroyd-B fluid 139 4.5. A fractional alternating-direction implicit method for a multiterm time-space fractional Bloch-Torrey equation in 3D 160 References 176 5. Fractional-order systems, numerical techniques, and applications 179 Fawang Liu, Pinghui Zhuang, Qingxia Liu, Minling Zheng, and Vo V. Anh 5.1. Introduction 179 5.2. Unstructured-mesh Galerkin finite element method for the 2D multiterm time-space fractional Bloch-Torrey equations on irregular convex domains 181 5.3. 5.4. 5.5. Finite difference/finite element method for a 2D multiterm timefractional mixed subdiffusion and diffusion-wave equation on convex domains 197 Alternating-direction implicit spectral Galerkin method for the multiterm time-space fractional diffusion equation in three dimensions 220 Space-time spectral method for the multiterm time-fractional diffusion equations 238 References 6. Chaos in fractional-order difference systems 254 257 Amina-Aicha Khennaoui, Adel Ouannas, Iqbal M. Batiha, and Viet-Thanh Pham 6.1. Introduction 257 6.2. Basic
concepts 259 6.3. Chaos in 2D fractional difference systems 262 6.4. Chaos in 3D fractional difference system 269 6.5. Concluding remarks and future works 277 Acknowledgment 277 References 283
vii Contents 7. A review on the realization of fractional-order devices to use as sensors and circuit elements for experimental studies and research 287 Árpit Sourav Mohapatra, Dina Anna John, and Karabi Biswas 7.1. Introduction 7.2. A brief history of the development of fractional-order elements (FOEs) 288 7.3. 290 Research work on single-component FOEs 7.4. Research work on multicomponent FOEs 7.5. Application of FOE as a sensor 7.6. Applications of FOE in circuits and systems 8. 287 300 312 320 7.7. Conclusion 336 References 338 FPAA-based implementation of fractional-order multidirectional multiscroll chaotic oscillators 341 Alejandro Silva-Juarez, Esteban Tlelo-Cuautle, and Luis Gerardo de la Fraga 8.1. Introduction 8.2. Multidirectional and multiscroll chaotic oscillator 9. 341 344 8.3. Multidirectional and multiscroll FOCO 8.4. Implementation of a multidirectional and multiscroll FOCO by FPAA 8.5. Conclusion 360 References 372 A survey on memristor active emulation circuits in the fractional-order domain 375 351 370 Nariman A. Khalil, Lobna A. Said, Ahmed G. Radwan, and Ahmed M. Soliman 9.1. Introduction 375 9.2. Memristive theory 377 9.3. Memristor application 9.4. Different memristance emulation circuits 382 9.5. 387 PSPICE simulations and experimental results 383 9.6. Conclusion 403 Acknowledgment 403 References 405 10. Fractional-order oscillators based on a single Op-Amp 411 Nariman A. Khalil, Menna Mohsen, Gehad M. Ahmed, Lobna A. Said, Ahmed H. Madian, and Ahmed G. Radwan 10.1. Introduction 411 10.2. Fractional-order oscillators 417
viii Contents 10.3. Family of single-Op-Amp oscillators with two fractional-order capacitors 419 10.4. PSPICE simulation and experimental results 428 10.5. Conclusion 431 Acknowledgment 432 References 433 11. Fractional calculus in electronic circuits: a review 441 Agniv Tapadar, Farooq Ahmad Khanday, Siddhartha Sen, and AvishekAdhikary 11.1. Introduction 441 11.2. Fractional-order circuit elements or fractors 443 11.3. Fractional-order RLC circuits 448 11.4. Design of fractional-order filters 452 11.5. Fractional-order oscillators 462 11.6. Recent trends in FO circuit synthesis 466 11.7. Conclusion and discussion 474 References 474 12. Dynamics and implementation techniques of fractional-order neuron models: a survey 483 Mohammad Rafiq Dar, Naşir Ali Kant, and Farooq Ahmad Khanday 12.1. Introduction 483 12.2. Neuron models 485 12.3. 486 Literature survey 12.4. General dynamical analysis of fractional-order model 494 12.5. 498 Dynamical investigation of the Hindmarsh-Rose neuron model 12.6. Implementation techniques of fractional-order neuron models 503 12.7. Conclusion 506 References 506 13. Fractional calculus: applications in rheology 513 Meryeme Hassouna, El Hassan El Kinani, and Abdelaziz Ouhadan 13.1. Introduction 513 13.2. Fractional calculus and transforms 516 13.3. Rheology, basic concepts 520 13.4. Fractional calculus in rheology for viscoelastic materials 527 13.5. Some rheological fractional anti-Zener models with Weyl fractional derivative 530 13.6. 544 The (a, j8)-Burgers model with Caputo derivative 13.7. Conclusion 547 References 547
ix Contents 14. Introduction of new kernels and new models to solve the drawbacks of fractional integration/differentiation operators and classical fractional-order models 551 Jocelyn Sabatier 14.1. 14.2. 14.3. 14.4. 14.5. 14.6. Introduction 551 Fractional-order models and associated drawbacks Some new kernels Volterra equations 552 559 569 Other alternative models to capturepower-law type behaviors Conclusion Appendix 14.A References Index 571 576 577 582 587
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| adam_txt |
Contents List of contributors 1. A survey on numerical studies for fractional biological models and their optima) control ХІ 1 N.H. Sweilam and S.M. AL-Mekhlafi 1.1. 1.2. Introduction Primary definitions of fractional calculus 1 2 1.3. 1.4. Fractional optimal control problem A survey on fractional biological models and their optimal control 3 4 1.5. 1.6. A survey on numerical methods for solving fractional optimal control biological models A novel fractional-order malaria mathematical model 7 13 1.7. 1.8. HFOCP Numerical experiment and discussion 16 25 1.9. Conclusions 26 References 2. A collection of interdisciplinary applications of fractional-order circuits 30 35 Panagiotis Berisiąs, Stavroula Kapoulea, Costas Psychalinos, and Ahmed S. Elwakil 3. 2.1. 2.2. Introduction Implementation of the approximated Laplacian operator 35 36 2.3. 2.4. Biomedical signal processing applications Bio-impedance applications 41 51 2.5. Sensor applications 2.6. Conclusions and discussion Acknowledgments 63 66 67 References 67 Fractional-order control 71 Ivo Petráš 3.1. Introduction 3.2. 3.3. 3.4. Fractional-order systems and controllers New fractional-order control techniques Discussion and conclusions Acknowledgment References 71 73 81 101 103 103 v
Contents VI 4. Fractional-order systems, numerical techniques, and applications 107 Fawang Liu, Pinghui Zhuang, Qingxia Liu, Minling Zheng, and Vo V. Anh 4.1. introduction 107 4.2. Numerical methods for solving the multiterm time-fractional diffusion-wave equation 112 4.3. Analytical solution of the multiterm time-fractional differential equation and application to unsteady flow of generalized viscoelastic fluid 121 4.4. Numerical analysis of multiterm time-fractional viscoelastic nonNewtonian fluid models for simulating unsteady MHD Couette flow of generalized Oldroyd-B fluid 139 4.5. A fractional alternating-direction implicit method for a multiterm time-space fractional Bloch-Torrey equation in 3D 160 References 176 5. Fractional-order systems, numerical techniques, and applications 179 Fawang Liu, Pinghui Zhuang, Qingxia Liu, Minling Zheng, and Vo V. Anh 5.1. Introduction 179 5.2. Unstructured-mesh Galerkin finite element method for the 2D multiterm time-space fractional Bloch-Torrey equations on irregular convex domains 181 5.3. 5.4. 5.5. Finite difference/finite element method for a 2D multiterm timefractional mixed subdiffusion and diffusion-wave equation on convex domains 197 Alternating-direction implicit spectral Galerkin method for the multiterm time-space fractional diffusion equation in three dimensions 220 Space-time spectral method for the multiterm time-fractional diffusion equations 238 References 6. Chaos in fractional-order difference systems 254 257 Amina-Aicha Khennaoui, Adel Ouannas, Iqbal M. Batiha, and Viet-Thanh Pham 6.1. Introduction 257 6.2. Basic
concepts 259 6.3. Chaos in 2D fractional difference systems 262 6.4. Chaos in 3D fractional difference system 269 6.5. Concluding remarks and future works 277 Acknowledgment 277 References 283
vii Contents 7. A review on the realization of fractional-order devices to use as sensors and circuit elements for experimental studies and research 287 Árpit Sourav Mohapatra, Dina Anna John, and Karabi Biswas 7.1. Introduction 7.2. A brief history of the development of fractional-order elements (FOEs) 288 7.3. 290 Research work on single-component FOEs 7.4. Research work on multicomponent FOEs 7.5. Application of FOE as a sensor 7.6. Applications of FOE in circuits and systems 8. 287 300 312 320 7.7. Conclusion 336 References 338 FPAA-based implementation of fractional-order multidirectional multiscroll chaotic oscillators 341 Alejandro Silva-Juarez, Esteban Tlelo-Cuautle, and Luis Gerardo de la Fraga 8.1. Introduction 8.2. Multidirectional and multiscroll chaotic oscillator 9. 341 344 8.3. Multidirectional and multiscroll FOCO 8.4. Implementation of a multidirectional and multiscroll FOCO by FPAA 8.5. Conclusion 360 References 372 A survey on memristor active emulation circuits in the fractional-order domain 375 351 370 Nariman A. Khalil, Lobna A. Said, Ahmed G. Radwan, and Ahmed M. Soliman 9.1. Introduction 375 9.2. Memristive theory 377 9.3. Memristor application 9.4. Different memristance emulation circuits 382 9.5. 387 PSPICE simulations and experimental results 383 9.6. Conclusion 403 Acknowledgment 403 References 405 10. Fractional-order oscillators based on a single Op-Amp 411 Nariman A. Khalil, Menna Mohsen, Gehad M. Ahmed, Lobna A. Said, Ahmed H. Madian, and Ahmed G. Radwan 10.1. Introduction 411 10.2. Fractional-order oscillators 417
viii Contents 10.3. Family of single-Op-Amp oscillators with two fractional-order capacitors 419 10.4. PSPICE simulation and experimental results 428 10.5. Conclusion 431 Acknowledgment 432 References 433 11. Fractional calculus in electronic circuits: a review 441 Agniv Tapadar, Farooq Ahmad Khanday, Siddhartha Sen, and AvishekAdhikary 11.1. Introduction 441 11.2. Fractional-order circuit elements or fractors 443 11.3. Fractional-order RLC circuits 448 11.4. Design of fractional-order filters 452 11.5. Fractional-order oscillators 462 11.6. Recent trends in FO circuit synthesis 466 11.7. Conclusion and discussion 474 References 474 12. Dynamics and implementation techniques of fractional-order neuron models: a survey 483 Mohammad Rafiq Dar, Naşir Ali Kant, and Farooq Ahmad Khanday 12.1. Introduction 483 12.2. Neuron models 485 12.3. 486 Literature survey 12.4. General dynamical analysis of fractional-order model 494 12.5. 498 Dynamical investigation of the Hindmarsh-Rose neuron model 12.6. Implementation techniques of fractional-order neuron models 503 12.7. Conclusion 506 References 506 13. Fractional calculus: applications in rheology 513 Meryeme Hassouna, El Hassan El Kinani, and Abdelaziz Ouhadan 13.1. Introduction 513 13.2. Fractional calculus and transforms 516 13.3. Rheology, basic concepts 520 13.4. Fractional calculus in rheology for viscoelastic materials 527 13.5. Some rheological fractional anti-Zener models with Weyl fractional derivative 530 13.6. 544 The (a, j8)-Burgers model with Caputo derivative 13.7. Conclusion 547 References 547
ix Contents 14. Introduction of new kernels and new models to solve the drawbacks of fractional integration/differentiation operators and classical fractional-order models 551 Jocelyn Sabatier 14.1. 14.2. 14.3. 14.4. 14.5. 14.6. Introduction 551 Fractional-order models and associated drawbacks Some new kernels Volterra equations 552 559 569 Other alternative models to capturepower-law type behaviors Conclusion Appendix 14.A References Index 571 576 577 582 587 |
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| spelling | Fractional order systems an overview of mathematics, design, and applications for engineers edited by Ahmed G. Radwan, Farooq Ahmad Khanday, Lobna A. Said Amsterdam Academic Press 2021 xiii, 598 Seiten Illustratienen, Diagramme 23 cm txt rdacontent n rdamedia nc rdacarrier Emerging methodologies and applications in modelling, identification and control 1 Intelligent control systems / Mathematics Fractional calculus Mathematical optimization Fractional calculus fast Mathematical optimization fast Regelungssystem (DE-588)4134712-2 gnd rswk-swf Regelungssystem (DE-588)4134712-2 s DE-604 Radwan, Ahmed Gharib Sonstige (DE-588)1124479414 oth Khanday, Farooq Ahmad ca. 20./21. Jh. Sonstige (DE-588)1252435975 oth Said, Lobna A. ca. 20./21. Jh. Sonstige (DE-588)1252436505 oth Emerging methodologies and applications in modelling, identification and control 1 (DE-604)BV047855516 1 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033041514&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Fractional order systems an overview of mathematics, design, and applications for engineers Emerging methodologies and applications in modelling, identification and control Intelligent control systems / Mathematics Fractional calculus Mathematical optimization Fractional calculus fast Mathematical optimization fast Regelungssystem (DE-588)4134712-2 gnd |
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| title | Fractional order systems an overview of mathematics, design, and applications for engineers |
| title_auth | Fractional order systems an overview of mathematics, design, and applications for engineers |
| title_exact_search | Fractional order systems an overview of mathematics, design, and applications for engineers |
| title_exact_search_txtP | Fractional order systems an overview of mathematics, design, and applications for engineers |
| title_full | Fractional order systems an overview of mathematics, design, and applications for engineers edited by Ahmed G. Radwan, Farooq Ahmad Khanday, Lobna A. Said |
| title_fullStr | Fractional order systems an overview of mathematics, design, and applications for engineers edited by Ahmed G. Radwan, Farooq Ahmad Khanday, Lobna A. Said |
| title_full_unstemmed | Fractional order systems an overview of mathematics, design, and applications for engineers edited by Ahmed G. Radwan, Farooq Ahmad Khanday, Lobna A. Said |
| title_short | Fractional order systems |
| title_sort | fractional order systems an overview of mathematics design and applications for engineers |
| title_sub | an overview of mathematics, design, and applications for engineers |
| topic | Intelligent control systems / Mathematics Fractional calculus Mathematical optimization Fractional calculus fast Mathematical optimization fast Regelungssystem (DE-588)4134712-2 gnd |
| topic_facet | Intelligent control systems / Mathematics Fractional calculus Mathematical optimization Regelungssystem |
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