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Mathematical 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 Elsevier Radarweg29,POBox211,1000AEAmsterdam,Netherlands TheBoulevard,LangfordLane,Kidlington,OxfordOX51GB,UnitedKingdom 50HampshireStreet,5thFloor,Cambridge,MA02139,UnitedStates Copyrightr2018ElsevierInc.Allrightsreserved. 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Practitionersandresearchersmustalwaysrelyontheirownexperienceandknowledgeinevaluatingand usinganyinformation,methods,compounds,orexperimentsdescribedherein.Inusingsuchinformation ormethodstheyshouldbemindfuloftheirownsafetyandthesafetyofothers,includingpartiesfor whomtheyhaveaprofessionalresponsibility. Tothefullestextentofthelaw,neitherthePublishernortheauthors,contributors,oreditors,assumeany liabilityforanyinjuryand/ordamagetopersonsorpropertyasamatterofproductsliability,negligence orotherwise,orfromanyuseoroperationofanymethods,products,instructions,orideascontainedin thematerialherein. BritishLibraryCataloguing-in-PublicationData AcataloguerecordforthisbookisavailablefromtheBritishLibrary LibraryofCongressCataloging-in-PublicationData AcatalogrecordforthisbookisavailablefromtheLibraryofCongress ISBN:978-0-12-813592-1 ForInformationonallElsevierpublications visitourwebsiteathttps://www.elsevier.com/books-and-journals Publisher:MaraConner AcquisitionEditor:SonniniR.Yura EditorialProjectManager:PeterJardim ProductionProjectManager:VijayarajPurushothaman CoverDesigner:MatthewLimbert TypesetbyMPSLimited,Chennai,India 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 systems, 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 applications 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 fractional 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 control,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 science. 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 science, 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 systems, 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