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 Engineering Science Reference (an imprint of IGI Global) 701 E. Chocolate Avenue Hershey PA, USA 17033 Tel: 717-533-8845 Fax: 717-533-8661 E-mail: [email protected] Web site: http://www.igi-global.com Copyright © 2020 by IGI Global. All rights reserved. No part of this publication may be reproduced, stored or distributed in any form or by any means, electronic or mechanical, including photocopying, without written permission from the publisher. Product or company names used in this set are for identification purposes only. Inclusion of the names of the products or companies does not indicate a claim of ownership by IGI Global of the trademark or registered trademark. 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) British Cataloguing in Publication Data A Cataloguing in Publication record for this book is available from the British Library. All work contributed to this book is new, previously-unpublished material. The views expressed in this book are those of the authors, but not necessarily of the publisher. For electronic access to this publication, please contact: [email protected]. 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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