Fractional-order Modelling of Dynamic Systems with Applications in Optimization, Signal Processing and Control introduces applications from a design perspective, helping readers plan and design their own applications. The book includes the different techniques employed to design fractional-order systems/devices comprehensively and straightforwardly. Furthermore, mathematics is available in the literature on how to solve fractional-order calculus for system applications. This book introduces the mathematics that has been employed explicitly for fractional-order systems. It will prove an excellent material for students and scholars who want to quickly understand the field of fractional-order systems and contribute to its different domains and applications.
Fractional-order systems are believed to play an essential role in our day-to-day activities. Therefore, several researchers around the globe endeavor to work in the different domains of fractional-order systems. The efforts include developing the mathematics to solve fractional-order calculus/systems and to achieve the feasible designs for various applications of fractional-order systems.
1. 1.1: Introduction - p. 1 2. 1.2: Continuous and discrete symmetry for classical differential equations - p. 2 3. 1.3: Continuous symmetry for fractional differential equation - p. 14 4. 1.4: Discrete symmetry for fractional Harry Dym equation - p. 30 5. 1.5: Conclusion - p. 33 6. Chapter Two Some theoretical and computation results about COVID-19 by using a fractional-order mathematical model - p. 37 7. 2.1: Introduction - p. 37 8. 2.2: Background materials - p. 42 9. 2.3: Main work - p. 46 10. 2.4: Series solution of the considered system (2.2) under normal Caputo derivative - p. 52 11. 2.5: General series solution of the considered system (2.3) - p. 58 12. Declaration of competing interest - p. 65 13. Chapter Three Spatial-fractional derivatives for fluid flow and transport phenomena - p. 69 14. Chapter Four On the hybrid fractional chaotic systems: a numerical approach - p. 97 15. Chapter Five Iterative processes with fractional derivatives - p. 119 16. 5.1: Introduction - p. 119 17. 5.2: Preliminary concepts - p. 120 18. 5.3: Design and analysis of iterative methods using fractional derivatives - p. 123 19. 5.4: Numerical analysis of the proposed methods - p. 132 20. 5.5: Concluding remarks - p. 144 21. Chapter Six Design of fractional-order finite-time sliding mode controllers for quadrotor UAVs subjected to disturbances and uncertainties - p. 151 22. Chapter Seven Performance evaluation of fractional character vector control applied for doubly fed induction generator operating in a network-connected wind power system - p. 179 23. Chapter Eight Finite time synchronization of discontinuous fractional order Cohen–Grossberg memristive neural networks with discrete delays under sliding mode control strategies - p. 213 24. 8.1: Introduction - p. 213 25. 8.2: Preliminaries - p. 217 26. 8.3: Main results - p. 226 27. 8.4: A numerical example - p. 239 28. 8.5: Conclusions - p. 244 29. Chapter Nine Variable-order control systems: a steady-state error analysis - p. 249 30. Chapter Ten Theoretical study in conformal thermal antennas optimized by a fractional energy - p. 271 31. Chapter Eleven Optimal design of fractional-order Butterworth filter with improved accuracy and stability margin - p. 293 32. Chapter Twelve Pseudospectral methods for the Riesz space-fractional Schrödinger equation - p. 323 33. Chapter Thirteen Transmission line modeling by fractional and topological generalization of the telegrapher's equation - p. 355 34. 13.1: Classical and fractional telegrapher's equations - p. 355 35. 13.2: Reduction of fractional telegrapher's equations to special cases - p. 363 36. 13.3: Transmission line model - p. 366 37. 13.4: Transmission line in transient regime - p. 373 38. 13.5: Transmission line in steady-state regime and its frequency characteristics - p. 382 39. Appendix 13.A: - p. 393 40. Chapter Fourteen System approach for the frequency analysis of a fractional-order acoustic tube: application for the resonator of the flute instrument - p. 403 41. Chapter Fifteen Fractional-order dynamics to study neuronal function - p. 429 42. Chapter Sixteen Modeling woody plant tissue using different fractional-order circuits - p. 457 43. Chapter Seventeen Analog and digital implementation of fractional-order FitzHugh–Nagumo (FO-FHN) neuron model - p. 475 44. Index - p. 505
Fractional-order Modelling of Dynamic Systems with Applications in Optimization, Signal Processing and Control introduces applications from a design perspective, helping readers plan and design their own applications. The book includes the different techniques employed to design fractional-order systems/devices comprehensively and straightforwardly. Furthermore, mathematics is available in the literature on how to solve fractional-order calculus for system applications. This book introduces the mathematics that has been employed explicitly for fractional-order systems. It will prove an excellent material for students and scholars who want to quickly understand the field of fractional-order systems and contribute to its different domains and applications.
Fractional-order systems are believed to play an essential role in our day-to-day activities. Therefore, several researchers around the globe endeavor to work in the different domains of fractional-order systems. The efforts include developing the mathematics to solve fractional-order calculus/systems and to achieve the feasible designs for various applications of fractional-order systems.
1. 1.1: Introduction - p. 1 2. 1.2: Continuous and discrete symmetry for classical differential equations - p. 2 3. 1.3: Continuous symmetry for fractional differential equation - p. 14 4. 1.4: Discrete symmetry for fractional Harry Dym equation - p. 30 5. 1.5: Conclusion - p. 33 6. Chapter Two Some theoretical and computation results about COVID-19 by using a fractional-order mathematical model - p. 37 7. 2.1: Introduction - p. 37 8. 2.2: Background materials - p. 42 9. 2.3: Main work - p. 46 10. 2.4: Series solution of the considered system (2.2) under normal Caputo derivative - p. 52 11. 2.5: General series solution of the considered system (2.3) - p. 58 12. Declaration of competing interest - p. 65 13. Chapter Three Spatial-fractional derivatives for fluid flow and transport phenomena - p. 69 14. Chapter Four On the hybrid fractional chaotic systems: a numerical approach - p. 97 15. Chapter Five Iterative processes with fractional derivatives - p. 119 16. 5.1: Introduction - p. 119 17. 5.2: Preliminary concepts - p. 120 18. 5.3: Design and analysis of iterative methods using fractional derivatives - p. 123 19. 5.4: Numerical analysis of the proposed methods - p. 132 20. 5.5: Concluding remarks - p. 144 21. Chapter Six Design of fractional-order finite-time sliding mode controllers for quadrotor UAVs subjected to disturbances and uncertainties - p. 151 22. Chapter Seven Performance evaluation of fractional character vector control applied for doubly fed induction generator operating in a network-connected wind power system - p. 179 23. Chapter Eight Finite time synchronization of discontinuous fractional order Cohen–Grossberg memristive neural networks with discrete delays under sliding mode control strategies - p. 213 24. 8.1: Introduction - p. 213 25. 8.2: Preliminaries - p. 217 26. 8.3: Main results - p. 226 27. 8.4: A numerical example - p. 239 28. 8.5: Conclusions - p. 244 29. Chapter Nine Variable-order control systems: a steady-state error analysis - p. 249 30. Chapter Ten Theoretical study in conformal thermal antennas optimized by a fractional energy - p. 271 31. Chapter Eleven Optimal design of fractional-order Butterworth filter with improved accuracy and stability margin - p. 293 32. Chapter Twelve Pseudospectral methods for the Riesz space-fractional Schrödinger equation - p. 323 33. Chapter Thirteen Transmission line modeling by fractional and topological generalization of the telegrapher's equation - p. 355 34. 13.1: Classical and fractional telegrapher's equations - p. 355 35. 13.2: Reduction of fractional telegrapher's equations to special cases - p. 363 36. 13.3: Transmission line model - p. 366 37. 13.4: Transmission line in transient regime - p. 373 38. 13.5: Transmission line in steady-state regime and its frequency characteristics - p. 382 39. Appendix 13.A: - p. 393 40. Chapter Fourteen System approach for the frequency analysis of a fractional-order acoustic tube: application for the resonator of the flute instrument - p. 403 41. Chapter Fifteen Fractional-order dynamics to study neuronal function - p. 429 42. Chapter Sixteen Modeling woody plant tissue using different fractional-order circuits - p. 457 43. Chapter Seventeen Analog and digital implementation of fractional-order FitzHugh–Nagumo (FO-FHN) neuron model - p. 475 44. Index - p. 505
