Table Of ContentMathematical Techniques of Fractional
Order Systems
Mathematical
Techniques of
Fractional Order
Systems
Edited by
Ahmad Taher Azar
Facultyof Computersand Information,Benha University,
Benha,Egypt
Schoolof Engineering and Applied Sciences, Nile University,
Giza,Egypt
Ahmed G. Radwan
Engineering Mathematics and PhysicsDepartment,
Facultyof Engineering, Cairo University, Giza,Egypt
Nanoelectronics Integrated Systems Center (NISC),
Nile University, Cairo, Egypt
Sundarapandian Vaidyanathan
Research and DevelopmentCenter,Vel Tech University,
Chennai, India
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List of Contributors
AmrM.AbdelAty EngineeringMathematicsandPhysicsDepartment,Facultyof
Engineering,FayoumUniversity,ElFayoum,Egypt
SalwaK.Abd-El-Hafiz FacultyofEngineering,CairoUniversity,Giza,Egypt
NorelysAguila-Camacho UniversityofChile,Santiago,Chile
MohsenAlimi UniversityofKairouan,Kairouan,Tunisia
DaliaAllam FayoumUniversity,Fayoum,Egypt
AhmadTaherAzar FacultyofComputersandInformation,BenhaUniversity,
Benha, Egypt; School of Engineering and Applied Sciences, Nile University,
Giza,Egypt
PagavathigounderBalasubramaniam GandhigramRuralInstitute(Deemedtobe
University),Dindigul,TamilNadu,India
YassineBensafia MohandOulhadjUniversityofBouira,Bouira10000,Algeria
MuzaffarA.Bhat JamiaMilliaIslamia,NewDelhi,India
Y.Boukal Universite´ deLorraine,CosnesetRomain,France; Universite´ HassanII,
Casablanca, Maroc; Universite´ de Valenciennes et du Hainaut-Cambre´sis,
Famars,France
BachirBourouba UniversityofSe´tif,Se´tif19000,Algeria
DanieleCasagrande UniversityofUdine,Udine,Italy
M.Darouach Universite´ deLorraine,CosnesetRomain,France
SubirDas IndianInstituteofTechnology(BHU),Varanasi,UttarPradesh,India
ManuelA.Duarte-Mermoud UniversityofChile,Santiago,Chile
MagdyEteiba FayoumUniversity,Fayoum,Egypt
IbiyinkaA.Fuwape FederalUniversityofTechnology,Akure,Nigeria; Michael
andCeciliaIbruUniversity,Ughelli,Nigeria
GokulP.M. LodzUniversityofTechnology,Lodz,Poland
HanyN.Hassan BenhaFacultyofEngineering,BenhaUniversity,Benha,
Egypt; ImamAbdulrahmanBinFaisalUniversity,Dammam,SaudiArabia
SamarM.Ismail FacultyofInformationEngineeringandTechnology(IET),
GermanUniversityinCairo(GUC),Cairo,Egypt
TomaszKapitaniak LodzUniversityofTechnology,Lodz,Poland
KhatirKhettab MohamedBoudiafUniversityofM’sila,M’sila28000,Algeria
xvii
xviii ListofContributors
WiesławKrajewski SystemsResearchInstitute,PolishAcademyofSciences,
Warsaw,Poland
JitendraKumar InstrumentationandControlEngineeringDivision,Dwarka,New
Delhi,India
VineetKumar InstrumentationandControlEngineeringDivision,Dwarka,New
Delhi,India
Mat´ıasG.Mayol-Sua´rez UniversityofChile,Santiago,Chile
JoanaP.Neto UniversidadedeLisboa,Lisbon,Portugal
SamuelT.Ogunjo FederalUniversityofTechnology,Akure,Nigeria
KayodeS.Ojo UniversityofLagos,Lagos,Nigeria
AdelOuannas UniversityofLarbiTebessi,Tebessa,Algeria
AdelOunnas UniversityofLarbiTebessi,Tebessa,Algeria
Viet(cid:1)ThanhPham HanoiUniversityofScienceandTechnology,Hanoi,
Vietnam; LodzUniversityofTechnology,Lodz,Poland
N.E.Radhy Universite´ HassanII,Casablanca,Maroc
AhmedG.Radwan FacultyofEngineering,CairoUniversity,Egypt; Nanoelectronics
IntegratedSystemsCenter(NISC),NileUniversity,Cairo,Egypt
KamalPalSinghRana InstrumentationandControlEngineeringDivision,Dwarka,
NewDelhi,India
AbdelwahebRebai UniversityofSfax,Sfax,Tunisia
AhmedRhif UniversityofCarthage,LaMarsa,Tunisia
LobnaA.Said Nano-ElectronicsIntegratedSystemsCenter(NISC),NileUniversity,
Giza,Egypt
T.Sathiyaraj GandhigramRuralInstitute(DeemedtobeUniversity),Dindigul,
TamilNadu,India
WafaaS.Sayed FacultyofEngineering,CairoUniversity,Giza,Egypt
MouradS.Semary BenhaFacultyofEngineering,BenhaUniversity,Benha,Egypt
FernandoE.Serranot CentralAmericanTechnicalUniversity(UNITEC),
Tegucigalpa,Honduras
BharatB.Sharma NationalInstituteofTechnology,Hamirpur,HimachalPradesh,
India
ManojK.Shukla NationalInstituteofTechnology,Hamirpur,HimachalPradesh,
India; LovelyProfessionalUniversity,Punjab,India
ShikhaSingh JamiaMilliaIslamia,NewDelhi,India
MayankSrivastava IndianInstituteofTechnology(BHU),Varanasi,UttarPradesh,
India
HamedTaghavian SharifUniversityofTechnology,Tehran,Iran
ListofContributors xix
PeachimuthuTamilalagan AmritaVishwaVidyapeetham(Deemedtobe
University),Coimbatore,TamilNadu,India
MohammadSalehTavazoei SharifUniversityofTechnology,Tehran,Iran
SundarapandianVaidyanathan VelTechUniversity,Chennai,TamilNadu,India
DuarteVale´rio UniversidadedeLisboa,Lisbon,Portugal
UmbertoViaro UniversityofUdine,Udine,Italy
SusanaVinga UniversidadedeLisboa,Lisbon,Portugal
ChristosVolos AristotleUniversityofThessaloniki,Thessaloniki,Greece
VijayK.Yadav IndianInstituteofTechnology(BHU),Varanasi,UttarPradesh,
India
DaliaYousri FayoumUniversity,Fayoum,Egypt
M.Zasadzinski Universite´ deLorraine,CosnesetRomain,France
Preface
Fractional calculus, as generalization of integer order integration and differ-
entiation to its noninteger (fractional) order counterpart, has proved to be a
valuable tool in the modeling of many physical phenomena and engineering
problems. Fractional derivatives provide an excellent instrument for the
description of memory and hereditary properties of various materials and
processes.
The main reason for using integer order models was the absence of solu-
tion methods for fractional differential equations. The advantages or the real
objectsofthefractional ordersystemsarethatwe have moredegrees offree-
dom in the model and that a “memory” is included in the model. One of the
very important areas of application of fractional calculus is the chaos theory.
Chaos is a very interesting nonlinear phenomenon which has been inten-
sively studied. It is found to be useful or has great application potential in
many fields such as secure communication, data encryption, financial sys-
tems, and biomedical engineering. The research efforts have been devoted to
chaos control and chaos synchronization problems in nonlinear science
becauseofits extensive applications.
Recently, studying fractional order systems has become an active
research area. The chaotic dynamics of fractional order systems began to
attract much attention in recent years. It has been shown that the fractional
order systems can also behave chaotically, such as the fractional order
Chua’s system, the fractional order Lorenz system, the fractional order Chen
system, the fractional order Ro¨ssler system, the fractional order modified
Duffing system, the fractional order Newton(cid:1)Leipnik system, the fractional
order Lotka(cid:1)Volterra system, and the fractional order Liu system.
Moreover, recent studies show that chaotic fractional order systems can also
be synchronized. Many scientists who are interested in this field have found
it to be a challenging research problem to achieve the synchronization of
fractional order chaotic systems, and this research area has potential applica-
tions insecurecommunicationand cryptography.
A wide variety of mathematical methods and techniques have been used
in this book to study the dynamics, control, design, and synchronization of
the fractional order control systems such as sliding mode controller, active
and adaptive control methods, fuzzy logic control, nonlinear control
xxi
xxii Preface
methods, fractional order discrete maps, multiswitching synchronization,
metaheuristic algorithms, backstepping control, etc.
ABOUT THE BOOK
The new Elsevier book, Mathematical Techniques of Fractional Order
Systems, consists of 21 contributed chapters by subject experts who are spe-
cialized in the various topics addressed in this book. The special chapters
have been brought out in this book after a rigorous review process in the
broad areas of mathematical techniques of fractional order systems. Special
importance was given to chapters offering practical solutions and novel
methods for the recent research problems in the mathematical modeling and
control applications of fractional order systems. This book discusses trends
and applications of mathematical models of fractional order systems in
engineering.
OBJECTIVES OF THE BOOK
This volume presents a selected collection of contributions on a focused
treatment of mathematical techniques for fractional order systems. The book
also discusses multidisciplinary applications in electrical engineering, control
engineering, mechanical engineering, and computer science. Both novice and
expert readers should find this book a useful reference in the field of frac-
tional order systems.
ORGANIZATION OF THE BOOK
This well-structured bookconsists of21 fullchapters.
BOOK FEATURES
(cid:1) The book chapters deal with the recent research problems in the areas of
fractional order systems.
(cid:1) The book chapters present various mathematical techniques for fractional
order systems such as active control, adaptive control, backstepping con-
trol,nonlinearcontrol, fuzzy logic control, metaheuristic algorithms, etc.
(cid:1) The book chapters contain a good literature survey with a long list of
references.
(cid:1) Thebookchaptersare well-writtenwith agoodexpositionofthe research
problem, methodology, block diagrams, andmathematical techniques.
(cid:1) The book chapters are lucidly illustrated with numerical examples and
simulations.
(cid:1) The book chapters discuss details of engineering applications and future
research areas.
Preface xxiii
AUDIENCE
The book is primarily meant for researchers from academia and industry,
who are working on fractional order systemsin the research areas—electrical
engineering, control engineering, mechanical engineering, and computer sci-
ence. The book can also be used at the graduate or advanced undergraduate
level as a text-book or major reference for courses such as power systems,
control systems, electrical devices, scientific modeling, computational sci-
ence, andmany others.
ACKNOWLEDGMENTS
As the editors, we hope that the chapters in this well-structured book will
stimulate further research in mathematical techniques of fractional order sys-
tems, and utilize them inreal-worldapplications.
We hope sincerely that this book, covering so many different topics, will
be very usefulfor all readers.
We would like to thank all the reviewers for their diligence in reviewing
the chapters.
Special thanks go toElsevier,especially the book Editorial team.
AhmadTaherAzar
FacultyofComputersandInformation,BenhaUniversity,
Benha,Egypt;SchoolofEngineeringandAppliedSciences,
NileUniversity,Giza,Egypt
AhmedG. Radwan
EngineeringMathematicsandPhysicsDepartment,FacultyofEngineering,
CairoUniversity,Giza,Egypt;NanoelectronicsIntegratedSystemsCenter(NISC),
NileUniversity,Cairo,Egypt
Sundarapandian Vaidyanathan
ResearchandDevelopmentCenter,VelTechUniversity,Chennai,India
