Fractional Order Systems and Applications in Engineering

1st Edition - November 17, 2022
Imprint: Academic Press
Editors: Dumitru Baleanu, Valentina Emilia Balas, Praveen Agarwal
Language: English
Paperback ISBN:
9 7 8 - 0 - 3 2 3 - 9 0 9 5 3 - 2
eBook ISBN:
9 7 8 - 0 - 3 2 3 - 9 0 9 5 4 - 9

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… Read more

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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.

Cover image
Title page
Table of Contents
Copyright
Contributors
Preface
Chapter 1: Complete synchronization of the time-fractional Chua reaction–diffusion system
Abstract
1.1. Introduction
1.2. Proposed system model
1.3. Free diffusion case: equilibria and stability
1.4. Spatio-temporal synchronization
1.5. Results and discussion
1.6. Concluding remarks
References
Chapter 2: New nonsymmetric and parametric divergences with particular cases
Abstract
2.1. Introduction
2.2. New information divergence measures
2.3. Divergence measures in the form of new series
2.4. Relations among divergence measures
2.5. Parametric measure of information
2.6. Concluding remarks
References
Chapter 3: Analytical solutions of some fractional diffusion boundary value problems
Abstract
3.1. Introduction
3.2. Definitions
3.3. Elementary results
3.4. Temperature distribution in finite solid circular cylinder
3.5. Particular case
3.6. Temperature distribution in finite hollow circular cylinder
3.7. Particular cases
References
Chapter 4: An enhanced hybrid stochastic fractal search FOPID for speed control of DC motor
Abstract
4.1. Introduction
4.2. Modeling of DC motor
4.3. Controller design and objective function
4.4. Proposed hybrid stochastic fractal search
4.5. Proposed HSFS-FOPID approach for speed control of DC motor
4.6. Modeling of DC motor with HSFS-FOPID
4.7. Robustness analysis
4.8. Conclusion
References
Chapter 5: Fractional dynamics and metrics of deadly pandemic diseases
Abstract
5.1. Introduction
5.2. Fractional model formulation
5.3. Basic reproduction number
5.4. Stability of equilibrium states
5.5. Discussion of results
5.6. Conclusion
References
Chapter 6: A numerical technique for solving fractional Benjamin–Bona–Mahony–Burgers equations with bibliometric analysis
Abstract
6.1. Introduction
6.2. Preliminaries
6.3. Riemann–Liouville pseudooperational matrix of Müntz–Legendre polynomials
6.4. Computational method
6.5. Convergence analysis
6.6. Numerical examples
6.7. Conclusion
References
Chapter 7: Some roots and paths in the fractional calculus developing environment
Abstract
Funding
Acknowledgements
7.1. Fractional calculus: historical touch and mathematical context. Definitions
7.2. New families of evolution equations. Dirac equations and fractional calculus
7.3. Numerical algorithms. Cloud computing
7.4. Atmospheric dust modeling
7.5. Electromagnetic waves. Fractal structures and metamaterials
References
Chapter 8: Accruement of nonlinear dynamical system and its dynamics: electronics and cryptographic engineering
Abstract
8.1. Introduction
8.2. Systems and their properties
8.3. Analog circuit imitations
8.4. Cryptography and security analysis
8.5. Conclusion
References
Chapter 9: Some new integral inequalities via generalized proportional fractional integral operators for the classes of m-logarithmically convex functions
Abstract
9.1. Introduction
9.2. New integral inequalities via generalized proportional integral operators
References
Chapter 10: Application and optimization of a robust fractional-order FOPI-FOPID automatic generation controller for a multiarea interconnected hybrid power system
Abstract
10.1. Introduction
10.2. Investigated PS
10.3. Controller
10.4. Optimization algorithm
10.5. Results and analysis
10.6. Conclusion
Appendix.
References
Chapter 11: Fourth-order fractional diffusion equations: constructs and memory kernel effects
Abstract
11.1. Introduction
11.2. Preliminaries
11.3. Solutions (to formally fractionalized models)
11.4. Solutions (to systematically fractionalized models)
11.5. A necessary discussion: what do the models developed mean
11.6. Conclusions
References
Chapter 12: Analysis of COVID-19 outbreak using GIS and SEIR model
Abstract
12.1. Introduction
12.2. Material and methods
12.3. Results and discussion
Conclusions
References
Chapter 13: Hidden chaotic attractors in fractional-order discrete-time systems
Abstract
13.1. Introduction
13.2. Basic tools
13.3. Fractional-order Hénon-like map with no equilibrium points
13.4. Conclusion
References
Chapter 14: Dynamical investigation and simulation of an incommensurate fractional-order model of COVID-19 outbreak with nonlinear saturated incidence rate
Abstract
14.1. Introduction
14.2. Background of Atangana–Baleanu operators
14.3. The SQIR model
14.4. Existence and uniqueness results
14.5. Basic reproduction number, existence, and stability of equilibria
14.6. Numerical approximation
14.7. Simulation and calibration of the fractional-order model
14.8. Conclusion
References
Chapter 15: Weak Pontryagin's maximum principle for optimal control problems involving a general analytic kernel
Abstract
Acknowledgements
15.1. Introduction
15.2. Preliminaries
15.3. Fundamental properties
15.4. Main results
References
Chapter 16: Computational half-sweep preconditioned Gauss–Seidel method for time-fractional diffusion equations
Abstract
16.1. Introduction
16.2. Preliminaries
16.3. Caputo's finite difference approximation
16.4. Analysis of stability of time fractional diffusion equations
16.5. Formulation of half-sweep preconditioned Gauss–Seidel
16.6. Numerical experiment
16.7. Conclusions
References
Chapter 17: Operational matrix approach for solving variable-order fractional integro-differential equations
Abstract
Acknowledgement
17.1. Introduction
17.2. Preliminaries and notations
17.3. Fourth kind Chebyshev polynomials and their shifted ones
17.4. Approach function
17.5. Convergence estimate
17.6. Operational matrices of differentiation and integration for solving VO-FIDEs
17.7. Computational examples and results analysis
17.8. Concluding remarks
References
Chapter 18: On basic Humbert confluent hypergeometric functions
Abstract
18.1. Introduction, definitions, basic concepts, and notations
18.2. q-Contiguous function relations and q-recursion formulas for q-Humbert confluent hypergeometric functions Φ1
18.3. q-Contiguous function relations and q-recursion formulas for Φ2
18.4. q-Contiguous function relations and q-recursion formulas for Φ3
18.5. q-Contiguous function relations and q-recursion formulas for Ψ1
18.6. q-Contiguous function relations and q-recursion formulas of q-Humbert confluent hypergeometric functions Ψ2
18.7. q-Contiguous function relations and q-recursion formulas for Ξ1
18.8. q-Contiguous function relations and q-recursion formulas for Ξ2
References
Chapter 19: Derivatives of Horn's hypergeometric functions G1, G2, Γ1, and Γ2 with respect to their parameters
Abstract
Acknowledgements
19.1. Introduction, basic concepts, notations, and preliminaries
19.2. Derivatives of Φ1 with respect to their parameters
19.3. Derivatives of G2 with respect to their parameters
19.4. Derivatives of Γ1 with respect to their parameters
19.5. Derivatives of Γ2 with respect to the parameters
19.6. Applications
19.7. Concluding remarks and observations
References
Index

Dumitru Baleanu

Dumitru Baleanu is a professor at the Institute of Space Sciences, Magurele-Bucharest, Romania and a visiting staff member at the Department of Mathematics, Çankaya, University, Ankara, Turkey. He received his Ph.D. from the Institute of Atomic Physics in 1996. His fields of interest include Fractional Dynamics and its applications, Fractional Differential Equations and their applications, Discrete Mathematics, Image Processing, Bioinformatics, Mathematical Biology, Mathematical Physics, Soliton Theory, Lie Symmetry, Dynamic Systems on time scales, Computational Complexity, the Wavelet Method and its applications, Quantization of systems with constraints, the Hamilton-Jacobi Formalism, as well as geometries admitting generic and non-generic symmetries.

Affiliations and expertise

Professor, Institute of Space Sciences, Magurele-Bucharest, Romania

Valentina Emilia Balas

Dr. Valentina Emilia Balas is currently a Full Professor at the Department of Automatics and Applied Software at the Faculty of Engineering, “Aurel Vlaicu” University of Arad, Romania. She holds a PhD cum laude in applied electronics and telecommunications from the Polytechnic University of Timisoara. Dr. Balas is the author of more than 350 research papers in refereed journals and for international conferences. Her research interests cover intelligent systems, fuzzy control, soft computing, smart sensors, information fusion, modeling, and simulation. She is the Editor-in-Chief of the 'International Journal of Advanced Intelligence Paradigms' and the 'International Journal of Computational Systems Engineering', an editorial board member for several other national and international publications, as well as an expert evaluator for national and international projects and PhD theses. Dr. Balas is the Director of the Intelligent Systems Research Center and the Director of the Department of International Relations, Programs and Projects at the “Aurel Vlaicu” University of Arad. She served as the General Chair for nine editions of the International Workshop on Soft Computing Applications (SOFA) organized in 2005–2020 and held in Romania and Hungary. Dr. Balas participated in many international conferences as organizer, honorary chair, session chair, member in steering, advisory or international program committees, and keynote speaker. Now she is working on a national project funded by the European Union: BioCell-NanoART = Novel Bio-inspired Cellular Nano-Architectures. She is a member of the European Society for Fuzzy Logic and Technology, a member of the Society for Industrial and Applied Mathematics, a senior member of IEEE, a member of the IEEE Fuzzy Systems Technical Committee, the chair of Task Force 14 of the IEEE Emergent Technologies Technical Committee, a member of the IEEE Soft Computing Technical Committee. She is also the recipient of the "Tudor Tanasescu" prize from the Romanian Academy for contributions in the field of soft computing methods (2019).

Affiliations and expertise

Full Professor, Department of Automatics and Applied Software, Faculty of Engineering, "Aurel Vlaicu" University of Arad, Arad, Romania

Praveen Agarwal

Dr. Praveen Agarwal is Vice-Principal and Professor at Anand International College of Engineering, Jaipur, India. He is listed as the World's Top 2% Scientist in 2020, 2021, 2022, and 2023, released by Stanford University. In the 2023 ranking of best scientists worldwide announced by Research.com, he ranked 21st at the India level and 2436th worldwide in Mathematics. He is a Managing Editor of Book seriesMathematics for Sustainable Developments, Springer Nature,and Editor ofBook series Mathematical Modelling & Computational Method for Innovation, Taylor & Francis Group.

He published more than 350 papers in international reputed Journals.

Affiliations and expertise

Full Professor, Anand International College of Engineering, Jaipur India; Nonlinear DynamicsResearch Center (NDRC), Ajman University, Ajman, UAE; Peoples Friendship University of Russia (RUDN University), Russian Federation

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