Fractional Order Systems and Applications in Engineering

Fractional Order Systems and Applications in Engineering

1st Edition - November 17, 2022

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  • Editors: Dumitru Baleanu, Valentina Emilia Balas, Praveen Agarwal
  • eBook ISBN: 9780323909549
  • Paperback ISBN: 9780323909532

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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.

Key Features

  • Provides the most recent and up-to-date developments on the Fractional-order Systems and their analyzing process
  • Integrates recent advancements of modeling of real phenomena (on Fractional-order Systems) via different-different mathematical equations with demonstrated applications in numerous seemingly diverse and widespread fields of science and engineering
  • Provides readers with illustrative examples of how to use the presented theories of Fractional-order Systems in specific cases with associated MATLAB code


Academics (scientists, researchers, MSc. PhD. students) from the fields of Mathematics, Computer Science, Biology, Electrical Engineering, Applied Mathematics and Information Technology. The audience includes researchers and practitioners in any field that deals with systems sciences – modelling of complex systems, systems analysis and nonlinear systems. Academics, researchers, and industries working in the fields of control engineering, mechatronics, modelling, robotics, and simulation

Table of Contents

  • 1. Complete synchronization of the time-fractional Chua reaction–diffusion system
    2. New nonsymmetric and parametric divergences with particular cases
    3. Analytical solutions of some fractional diffusion boundary value problems
    4. An enhanced hybrid stochastic fractal search FOPID for speed control of DC motor
    5. Fractional dynamics and metrics of deadly pandemic diseases
    6. A numerical technique for solving fractional Benjamin–Bona–Mahony–Burgers equations with bibliometric analysis
    7. Some roots and paths in the fractional calculus developing environment
    8. Accruement of nonlinear dynamical system and its dynamics: electronics and cryptographic engineering
    9. Some new integral inequalities via generalized proportional fractional integral operators for the classes of m-logarithmically convex functions
    10. Application and optimization of a robust fractional-order FOPI-FOPID automatic generation controller for a multiarea interconnected hybrid power system
    11. Fourth-order fractional diffusion equations: constructs and memory kernel effects
    12. Analysis of COVID-19 outbreak using GIS and SEIR model
    13. Hidden chaotic attractors in fractional-order discrete-time systems
    14. Dynamical investigation and simulation of an incommensurate fractional-order model of COVID-19 outbreak with nonlinear saturated incidence rate
    15. Weak Pontryagin’s maximum principle for optimal control problems involving a general analytic kernel
    16. Computational half-sweep preconditioned Gauss–Seidel method for time-fractional diffusion equations
    17. Operational matrix approach for solving variable-order fractional integro-differential equations
    18. On basic Humbert confluent hypergeometric functions
    19. Derivatives of Horn’s hypergeometric functions G1, G2, >1, and >2 with respect to their parameters

Product details

  • No. of pages: 390
  • Language: English
  • Copyright: © Academic Press 2022
  • Published: November 17, 2022
  • Imprint: Academic Press
  • eBook ISBN: 9780323909549
  • Paperback ISBN: 9780323909532

About the Editors

Dumitru Baleanu

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 holds several other affiliations, including Adjunct Research Professor at the Nonlinear Dynamics Research Center (NDRC) at Ajman University, UAE, and Director of the International Centre for Basic and Applied Science, India. Dr. Agarwal is author/co-author of several books, including Advances in Real and Complex Analysis with Applications, Birkhäuser; Advances in Mathematical Inequalities and Applications, Birkhäuser; Fixed Point Theory in Metric Spaces: Recent Advances and Applications, Springer; A Study of New Trends and Analysis of Special Functions, Lambert Academic Publishing; Special Functions and Analysis of Differential Equations, Chapman & Hall CRC Press; Metric Structures and Fixed Point Theory, Chapman & Hall CRC Press; and Analysis of Infectious Disease Problems (Covid-19) and Their Global Impact, Springer. His research specialties include work on Fractional Calculus, applied mathematics, mathematical problems in engineering, and abstract and applied computational modelling and analysis. He is an Editor of many journals, including Applied Numerical Mathematics, Elsevier; Mathematical Methods in the Applied Sciences, Wiley; and is Editor-in-Chief of International Journal of Mathematical Research (IJMR). Dr. Agarwal has been a lead or guest editor for many journal special issues, including “Recent Trends in Mathematical Analysis and Their Applications” in Open Engineering, Lead Guest Editor of “New Trends in Special Functions and Real Analysis for Solving Complex Problems” in Journal of Mathematics, “Special Issue on Swarm Intelligence and Its Applications” in Scientific World Journal, “Special Issue on New Trends in Fractional Calculus and Its Applications in Engineering and Other Sciences” in Scientific World Journal, and “Special Issue on Artificial Intelligence and Its Applications” in Mathematical Problems in Engineering.

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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