Fractional Calculus: Applications

Roy Abi Zeid Daou (Editor)
Lebanese German University, Sahel Alma Campus, Keserwane, Lebanon

Xavier Moreau (Editor)
Université Bordeaux, 351, cours de la Libération, Talence – France

Series: Mathematics Research Developments
BISAC: MAT005000




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After presenting the first volume of this two-volume book, presenting a lot of mathematical and theoretical studies and research related to non-integer calculus, the second volume illustrates applications related to this domain. This volume is made up of 11 chapters. The first chapter presents the heuristic power of the non-integer differential operators in physics starting from the chaos to the emergence, the auto-organizations and the holistic rules. The second chapter shows the dynamics of the fractional order chaotic systems along with some applications.

The third chapter represents the pressure control of gas engines by non-integer order controllers by showing a novel trend in the application of the fractional calculus to automotive systems. Chapter 4 shows the way to model fractional order equations using state space modeling along with some applications. Another application related to this domain is the thermal diffusive interface. Chapter 5 shows the analysis of a semi-infinite diffuse plane medium along with the equations that model this medium, and some frequency and time domain responses. However, Chapter 6 treats this problem by controlling this plant using the well-known CRONE controller. Chapter 8 presents the adaptive second-order fractional sliding mode control with an application to a water tanks level system. Chapter 9 treats the mechanical aspect by showing the features of the fractional operators applied to this domain.

Also, Chapter Nine presents the theory of diffusive stresses based on the fractional advection-diffusion equation. The modeling of drug diffusion during general anesthesia using Fractional Calculus is shown in Chapter 10 and is considered as another application related to the biomedical field. Finally, Chapter 11 represents an overview of the fractional fuzzy controllers by showing the analysis, the synthesis and the implementation of this module. To sum up, this second volume presents applications of fractional calculus in several engineering domains as the thermal, the automotive, the mechanical, the biomedical and much more. Note that this volume was preceded by a first volume that focuses on the mathematical and theoretical aspects of fractional calculus.
(Imprint: Nova)

Foreword Alain Oustaloup


Chapter 1 - The Heuristic Power of the Non Integer Differential Operator in Physics: From Chaos to Emergence, Auto-Organisations and Holistic Rules (pp. 1-22)
Alain Le Méhauté (Physics Department. Kazan Federal University 420 008 Kazan, Russia)

Chapter 2 - Dynamics of Fractional Order Chaotic Systems (pp. 23-36)
Sachin Bhalekar (Department of Mathematics, Shivaji University, Kolhapur, India)

Chapter 3 - Pressure Control of CNG Engines by Non-integer Order Controllers: A New Trend in Application of Fractional Calculus to Automotive Systems (pp. 37-64)
Paolo Lino and Guido Maione (Dipartimento di Ingegneria Elettricaedell Informazione–Politecnico di Bari, Italy)

Chapter 4 - Linear Integer Order System Control by Fractional PI-State Feedback (pp. 65-92)
Rachid Mansouri, Maamar Bettayeb, Chahira Boussalem and Ubaid M. Al-Saggaf (University Mouloud Mammeri of Tizi-Ouzou, Algeria and others)

Chapter 5 - From the Formal Concept Analysis to the Numerical Simulation of the Thermal Diffusion Phenomena in a Finite Medium (pp. 93-122)
Riad Assaf, Roy Abi Zeid Daou, Xavier Moreau and Fady Christophy (University of Bordeaux, IMS Laboratory, UMR 5218 CNRS, 33405 Talence, Bordeaux, France and others)

Chapter 6 - Temperature Control of a Diffusive Medium Using the CRONE Approach (pp. 123-148)
Fady Christophy, Xavier Moreau, Roy Abi Zeid Daou and Riad Assaf (University of Bordeaux, Laboratory IMS, UMR 5218 CNRS, 33405 Talence, Bordeaux, France and others)

Chapter 7 - Adaptive Second-Order Fractional Sliding Mode Control with Application to Water Tanks Level Control (pp. 149-164)
Danial Senejohnny, Mohammadreza Faieghi and Hadi Delavari (Faculty of Electrical Engineering, Sharif University of Technology, Tehran, and Faculty of Electrical Engineering, Hamedan University of Technology, Hamedan, Iran and others)

Chapter 8 - Features of Fractional Operators Involving Fractional Derivatives and Their Applications to the Problems of Mechanics of Solids (pp. 165-226)
Yury A. Rossikhin and Marina V. Shitikova (Research Center on Dynamics of Solids, Voronezh State University of Architecture and Civil Engineering, Russia)

Chapter 9 - Theory of Diffusive Stresses Based on the Fractional Advection-Diffusion Equation (pp. 227-242)
Yuriy Povstenko (Institute of Mathematics and Computer Science, Jan D³ugosz University, Poland)

Chapter 10 - Modelling Drug Effect Using Fractional Calculus (pp. 243-258)
Clara M. Ionescu (Ghent University, Department of Electrical Energy, Systems and Automation, Belgium)

Chapter 11 - Fuzzy Fractional PID Controllers: Analysis, Synthesis and Implementation (pp. 259-288)
Ramiro S. Barbosa and Isabel S. Jesus (GECAD, Portugal)


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