Advanced Applications of Fractional Differential Operators to Science and Technology (Advances in Computer and Electrical Engineering)

423 Pages·2020·22.931 MB·English

by  Ahmed Ezzat Matouk

Advanced Applications
of Fractional Differential
Operators to Science and
Technology
Ahmed Ezzat Matouk
Majmaah University, Saudi Arabia
A volume in the Advances in Computer and
Electrical Engineering (ACEE) Book Series
Published in the United States of America by
IGI Global
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Library of Congress Cataloging-in-Publication Data
Names: Matouk, Ahmed Ezzat, 1976- editor.
Title: Advanced applications of fractional differential operators to
science and technology / Ahmed Ezzat Matouk, editor.
Description: Hershey, PA : Engineering Science Reference, an imprint of IGI
Global, [2020] | Includes bibliographical references and index. |
Summary: “This book examines fractional calculus and its application in
science, engineering, and technology”-- Provided by publisher.
Identifiers: LCCN 2019048562 (print) | LCCN 2019048563 (ebook) | ISBN
9781799831228 (hardcover) | ISBN 9781799831235 (paperback) | ISBN
9781799831242 (ebook)
Subjects: LCSH: Engineering mathematics. | Fractional differential
equations.
Classification: LCC TA347.D45 A37 2020 (print) | LCC TA347.D45 (ebook) |
DDC 515/.35--dc23
LC record available at https://lccn.loc.gov/2019048562
LC ebook record available at https://lccn.loc.gov/2019048563

This book is published in the IGI Global book series Advances in Computer and Electrical Engineering (ACEE) (ISSN:
2327-039X; eISSN: 2327-0403)
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All work contributed to this book is new, previously-unpublished material. The views expressed in this book are those of the
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For electronic access to this publication, please contact: [e-mail].
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ISSN:2327-039X
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To my family for their endless support.

Editorial Advisory Board
E.Ahmed,Mansoura University, Egypt
S.S.Askar,King Saud University, Saudi Arabia
A.M.A.El-Sayed,Alexandria University, Egypt
G.M.Mahmoud,Assiut University, Egypt
A.G.Radwan,Nile University, Egypt
FathallaA.Rihan,United Arab Emirates University, UAE


Table of Contents
Foreword.............................................................................................................................................xvi
Preface...............................................................................................................................................xviii
Section 1
Fractional-Order Calculus in Biological Models
Chapter 1
Fractional-OrderCalculusinAntimicrobialResistanceandWaningVaccination.................................1
E. Ahmed, Mansoura University, Egypt
Ahmed Ezzat Mohamed Matouk, Majmaah University, Saudi Arabia
Chapter 2
BifurcationandChaosinaDiscreteFractional-OrderPrey-PredatorSystemInvolvingAllee
Effect.....................................................................................................................................................21
George Maria Selvam A., Sacred Heart College (Autonomous), India
Janagaraj R., Sacred Heart College (Autonomous), India
Chapter 3
ApplicationofFractionalOptimalControlProblemsonSomeMathematicalBioscience..................41
Ismail Gad Ameen, South Valley University, Egypt
Hegagi Mohamed Ali, Aswan University, Egypt
Section 2
Chaotic Dynamics of Fractional-Order Systems
Chapter 4
DynamicsofSomeDiscretizedFractional-OrderDifferentialEquations............................................58
Sanaa Moussa Salman, Alexandria University, Egypt
Ahmed M. A. El-Sayed, Alexandria University, Egypt
Chapter 5
OntheInfluenceofFractionalDerivativeonChaosControlofaNewFractional-Order
HyperchaoticSystem..........................................................................................................................115
Ahmed Ezzat Mohamed Matouk, Majmaah University, Saudi Arabia


Chapter 6
SynchronizationofFractional-OrderHyperchaoticFinanceSystemsUsingSlidingModeControl
Techniques..........................................................................................................................................133
Sanjay Kumar, Acharya Narendra Dev College, University of Delhi, India & Amity School of
Engineering and Technology, Amity University, Patna, India
Ram Pravesh Prasad, Hansraj College, University of Delhi, India
Krishan Pal, Maharaja Agarsen College, University of Delhi, India
Mahendra Pratap Pal, Delhi College of Arts and Commerce, University of Delhi, India
Ajeet Singh, Satyawati College, University of Delhi, India
Section 3
Applications of Fractional Derivatives to Physics
Chapter 7
GeneralizedBrinkmanTypeDustyFluidModelforBloodFlow......................................................154
Muhammad Saqib, Universiti Teknologi Malaysia, Malaysia
Sharidan Shafie, Universiti Teknologi Malaysia, Malaysia
Ilyas Khan, College of Engineering, Majmaah University, Saudi Arabia
Chapter 8
RevisitingAnomalousg-FactorsforChargedLeptonsinaFractionalCoarse-GrainedApproach
WithAxiomaticLocalMetricDerivatives..........................................................................................171
José Weberszpil, Universidade Federal Rural do Rio de Janeiro, Brazil
José Abdalla Helayël-Neto, Centro Brasileiro de Pesquisas Físicas, Brazil
Chapter 9
PropertiesofSpatial-RotationTransformationsofFractionalDerivatives.........................................198
Ehab Malkawi, Physics Department, United Arab Emirates University, UAE
Chapter 10
OntheApproximateSolutionofCaputo-Riesz-FellerFractionalDiffusionEquation.......................224
Samir Shamseldeen, Faculty of Engineering, Mansoura University, Egypt
Ahmed Elsaid, Faculty of Engineering, Mansoura University, Egypt
Seham Madkour, Faculty of Engineering, Mansoura University, Egypt
Section 4
New Trends in Applied Mathematics
Chapter 11
GeneralizedFractionalOstrowski’sTypeInequalitiesInvolvingRiemann-LiouvilleFractional
Integration...........................................................................................................................................246
Ather Qayyum, Institute of Southern Punjab Multan, Pakistan
Muhammad Shoaib, Higher Colleges of Technology, UAE

Chapter 12
TheInvariantSubspaceMethodforSolvingFractionalPartialDifferentialEquations.....................267
Mohamed Soror Abdel Latif, Mansoura University, Egypt
Abass Hassan Abdel Kader, Mansoura University, Egypt
Chapter 13
ApparentMeasure,IntegralofRealOrder,andRelativeDimension.................................................283
Faycal Adda, Community College of Qatar, Qatar
Section 5
Applications of Fractional Calculus to Engineering
Chapter 14
Fractional-Order-BasedInferentialControl:ACaseStudyfortheLevelControlofThree
InteractingTankProcesses..................................................................................................................322
Abdul Wahid Nasir, CMR Institute of Technology, Bengaluru, India
Idamakanti Kasireddy, Vaagdevi College of Engineering, Warangal, India
Arun Kumar Singh, National Institute of Technology, Jamshedpur, India
Chapter 15
OntheApplicationofFractionalDerivativestotheStudyofMemristorDynamics.........................342
Rawid Banchuin, Siam University, Thailand
Compilation of References...............................................................................................................364
About the Contributors....................................................................................................................396
Index...................................................................................................................................................400
Detailed Table of Contents
Foreword.............................................................................................................................................xvi
Preface...............................................................................................................................................xviii
Section 1
Fractional-Order Calculus in Biological Models
Chapter 1
Fractional-OrderCalculusinAntimicrobialResistanceandWaningVaccination.................................1
E. Ahmed, Mansoura University, Egypt
Ahmed Ezzat Mohamed Matouk, Majmaah University, Saudi Arabia
Inthischapter,asimplemodelforcompetitionbetweendrugresistantanddrugsensitivebacteriais
given.So,amodelofantimicrobialresistance(AMR)andwaningvaccinationispresented.Themodel’s
steadystatesareobtained.Theconditionsoflocalstabilityoftheequilibriaarealsoderivedviathe
fractionalRouth-Hurwitzcriterion.Adiscretizationschemehasalsobeenappliedtotheproposed
fractional-ordermodeltoenhancethemodel’sadequacyandaccuracyofdescribingnaturalphenomena.
So,dynamicalbehaviorsoftheresultingdiscrete-timemodelarestudiedsuchaslocalstability,existence
ofNeimark-Sacker,andflipbifurcations.Furthermore,existenceofchaosinthediscrete-timemodelis
provedusingthetheoremgivenbyMarotto.Chaoticattractorsandroutestochaosarealsodepictedvia
variousnumericaltools.
Chapter 2
BifurcationandChaosinaDiscreteFractional-OrderPrey-PredatorSystemInvolvingAllee
Effect.....................................................................................................................................................21
George Maria Selvam A., Sacred Heart College (Autonomous), India
Janagaraj R., Sacred Heart College (Autonomous), India
Thischapterconsidersthediscretecounterpartofafractionalorderprey-predatorODEsysteminvolving
Alleeeffect.Severalmorerealisticmodelswereproposedtodescribenonlinearinteractionsbetween
speciesbyintroducingdifferenttypesfunctionalresponsesandAlleeeffect.Non-localpropertyof
fractionaldifferentialequationsisusefulinmodelingpopulationinteractionspossessingmemories.
Themodelunderinvestigationhasthreesteadystates,andthepositivesteadystateexistsundercertain
condition.Dynamicnatureofthemodelisdiscussedthroughlocalstabilityanalysis.Enquiryintothe
qualitativebehaviorofthemodelrevealsrichandcomplexdynamicsexhibitedbythediscrete-time
model.Moreover,thismodelundergoesNeimarkSackerbifurcationwhenthechosenparameterpasses