Fractional Order Systems and Applications in Engineering presents the use of fractional calculus (calculus of non-integer order) in the description and modelling of systems and in a range of control design and practical applications. The book covers the fundamentals of fractional calculus together with some analytical and numerical techniques, and provides MATLAB® codes for the simulation of fractional-order control (FOC) systems. The use of fractional calculus can improve and generalize well-established control methods and strategies. Many different FOC schemes are presented for control and dynamic systems problems. These extend to the challenging control engineering design problems of robust and nonlinear control. Practical material relating to a wide variety of applications including, among others, mechatronics, civil engineering, irrigation and water management, and biological systems is also provided. All the control schemes and applications are presented with either system simulation results or real experimental results, or both. Fractional Order Systems and Applications in Engineering introduces readers to the essentials of FOC and imbues them with a basic understanding of FOC concepts and methods. With this knowledge readers can extend their use of FOC in other industrial system applications, thereby expanding their range of disciplines by exploiting this versatile new set of control techniques.
1. 9.1 Introduction - p. page157 2. 9.2 New integral inequalities via generalized proportional integral operators - p. 161 3. References - p. 172 4. Chapter 10. Application and optimization of a robust fractional-order FOPI-FOPID automatic generation controller for a multiarea interconnected hybrid power system - p. 176 5. Chapter 11. Fourth-order fractional diffusion equations: constructs and memory kernel effects - p. 199 6. Chapter 12. Analysis of COVID-19 outbreak using GIS and SEIR model - p. 215 7. Chapter 13. Hidden chaotic attractors in fractional-order discrete-time systems - p. 227 8. Chapter 14. Dynamical investigation and simulation of an incommensurate fractional-order model of COVID-19 outbreak with nonlinear saturated incidence rate - p. 245 9. Weak Pontryagin's maximum principle for optimal control problems involving a general analytic kernel - p. 267 10. Chapter 16. Computational half-sweep preconditioned Gauss–Seidel method for time-fractional diffusion equations - p. 285 11. Chapter 17. Operational matrix approach for solving variable-order fractional integro-differential equations - p. 301 12. Chapter 18. On basic Humbert confluent hypergeometric functions - p. 319 13. Abstract - p. 319 14. 18.1 Introduction, definitions, basic concepts, and notations - p. page319 15. 18.2 q-Contiguous function relations and q-recursion formulas for q-Humbert confluent hypergeometric functions Φ1Φ1 - p. 321 16. 18.3 q-Contiguous function relations and q-recursion formulas for Φ2Φ2 - p. 328 17. 18.4 q-Contiguous function relations and q-recursion formulas for Φ3Φ3 - p. 331 18. 18.5 q-Contiguous function relations and q-recursion formulas for Ψ1Ψ1 - p. 334 19. 18.6 q-Contiguous function relations and q-recursion formulas of q-Humbert confluent hypergeometric functions Ψ2Ψ2 - p. 339 20. 18.7 q-Contiguous function relations and q-recursion formulas for Ξ1Ξ1 - p. 343 21. 18.8 q-Contiguous function relations and q-recursion formulas for Ξ2Ξ2 - p. 349 22. References - p. 352 23. Derivatives of Horn's hypergeometric functions G1G1, G2G2, Γ1Γ1, and Γ2Γ2 with respect to their parameters - p. 353 24. Abstract - p. 353 25. Acknowledgements - p. page353 26. 19.1 Introduction, basic concepts, notations, and preliminaries - p. page353 27. 19.2 Derivatives of Φ1Φ1 with respect to their parameters - p. 355 28. 19.3 Derivatives of G2G2 with respect to their parameters - p. 360 29. 19.4 Derivatives of Γ1Γ1 with respect to their parameters - p. 365 30. 19.5 Derivatives of Γ2Γ2 with respect to the parameters - p. 369 31. 19.6 Applications - p. 372 32. 19.7 Concluding remarks and observations - p. 373 33. References - p. 373 34. Index - p. 375
Fractional Order Systems and Applications in Engineering presents the use of fractional calculus (calculus of non-integer order) in the description and modelling of systems and in a range of control design and practical applications. The book covers the fundamentals of fractional calculus together with some analytical and numerical techniques, and provides MATLAB® codes for the simulation of fractional-order control (FOC) systems. The use of fractional calculus can improve and generalize well-established control methods and strategies. Many different FOC schemes are presented for control and dynamic systems problems. These extend to the challenging control engineering design problems of robust and nonlinear control. Practical material relating to a wide variety of applications including, among others, mechatronics, civil engineering, irrigation and water management, and biological systems is also provided. All the control schemes and applications are presented with either system simulation results or real experimental results, or both. Fractional Order Systems and Applications in Engineering introduces readers to the essentials of FOC and imbues them with a basic understanding of FOC concepts and methods. With this knowledge readers can extend their use of FOC in other industrial system applications, thereby expanding their range of disciplines by exploiting this versatile new set of control techniques.
1. 9.1 Introduction - p. page157 2. 9.2 New integral inequalities via generalized proportional integral operators - p. 161 3. References - p. 172 4. Chapter 10. Application and optimization of a robust fractional-order FOPI-FOPID automatic generation controller for a multiarea interconnected hybrid power system - p. 176 5. Chapter 11. Fourth-order fractional diffusion equations: constructs and memory kernel effects - p. 199 6. Chapter 12. Analysis of COVID-19 outbreak using GIS and SEIR model - p. 215 7. Chapter 13. Hidden chaotic attractors in fractional-order discrete-time systems - p. 227 8. Chapter 14. Dynamical investigation and simulation of an incommensurate fractional-order model of COVID-19 outbreak with nonlinear saturated incidence rate - p. 245 9. Weak Pontryagin's maximum principle for optimal control problems involving a general analytic kernel - p. 267 10. Chapter 16. Computational half-sweep preconditioned Gauss–Seidel method for time-fractional diffusion equations - p. 285 11. Chapter 17. Operational matrix approach for solving variable-order fractional integro-differential equations - p. 301 12. Chapter 18. On basic Humbert confluent hypergeometric functions - p. 319 13. Abstract - p. 319 14. 18.1 Introduction, definitions, basic concepts, and notations - p. page319 15. 18.2 q-Contiguous function relations and q-recursion formulas for q-Humbert confluent hypergeometric functions Φ1Φ1 - p. 321 16. 18.3 q-Contiguous function relations and q-recursion formulas for Φ2Φ2 - p. 328 17. 18.4 q-Contiguous function relations and q-recursion formulas for Φ3Φ3 - p. 331 18. 18.5 q-Contiguous function relations and q-recursion formulas for Ψ1Ψ1 - p. 334 19. 18.6 q-Contiguous function relations and q-recursion formulas of q-Humbert confluent hypergeometric functions Ψ2Ψ2 - p. 339 20. 18.7 q-Contiguous function relations and q-recursion formulas for Ξ1Ξ1 - p. 343 21. 18.8 q-Contiguous function relations and q-recursion formulas for Ξ2Ξ2 - p. 349 22. References - p. 352 23. Derivatives of Horn's hypergeometric functions G1G1, G2G2, Γ1Γ1, and Γ2Γ2 with respect to their parameters - p. 353 24. Abstract - p. 353 25. Acknowledgements - p. page353 26. 19.1 Introduction, basic concepts, notations, and preliminaries - p. page353 27. 19.2 Derivatives of Φ1Φ1 with respect to their parameters - p. 355 28. 19.3 Derivatives of G2G2 with respect to their parameters - p. 360 29. 19.4 Derivatives of Γ1Γ1 with respect to their parameters - p. 365 30. 19.5 Derivatives of Γ2Γ2 with respect to the parameters - p. 369 31. 19.6 Applications - p. 372 32. 19.7 Concluding remarks and observations - p. 373 33. References - p. 373 34. Index - p. 375
