Table Of ContentLecture Notes in Networks and Systems 415
Jagdev Singh · George A. Anastassiou ·
Dumitru Baleanu · Carlo Cattani ·
Devendra Kumar Editors
Advances in
Mathematical
Modelling,
Applied Analysis
and Computation
Proceedings of ICMMAAC 2021
Lecture Notes in Networks and Systems
Volume 415
SeriesEditor
JanuszKacprzyk,SystemsResearchInstitute,PolishAcademyofSciences,
Warsaw,Poland
AdvisoryEditors
FernandoGomide,DepartmentofComputerEngineeringandAutomation—DCA,
SchoolofElectricalandComputerEngineering—FEEC,UniversityofCampinas—
UNICAMP,SãoPaulo,Brazil
OkyayKaynak,DepartmentofElectricalandElectronicEngineering,
BogaziciUniversity,Istanbul,Turkey
DerongLiu,DepartmentofElectricalandComputerEngineering,University
ofIllinoisatChicago,Chicago,USA
InstituteofAutomation,ChineseAcademyofSciences,Beijing,China
WitoldPedrycz,DepartmentofElectricalandComputerEngineering,Universityof
Alberta,Alberta,Canada
SystemsResearchInstitute,PolishAcademyofSciences,Warsaw,Poland
MariosM.Polycarpou,DepartmentofElectricalandComputerEngineering,
KIOSResearchCenterforIntelligentSystemsandNetworks,UniversityofCyprus,
Nicosia,Cyprus
ImreJ.Rudas,ÓbudaUniversity,Budapest,Hungary
JunWang,DepartmentofComputerScience,CityUniversityofHongKong,
Kowloon,HongKong
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· ·
Jagdev Singh George A. Anastassiou
· ·
Dumitru Baleanu Carlo Cattani Devendra Kumar
Editors
Advances in Mathematical
Modelling, Applied Analysis
and Computation
Proceedings of ICMMAAC 2021
Editors
JagdevSingh GeorgeA.Anastassiou
DepartmentofMathematics DepartmentofMathematics
JECRCUniversity UniversityofMemphis
Jaipur,India Tennessee,TN,USA
DumitruBaleanu CarloCattani
DepartmentofMathematics EngineeringSchool,DEIM
CankayaUniversity UniversityofTuscia
Ankara,Turkey Viterbo,Italy
DevendraKumar
DepartmentofMathematics
UniversityofRajasthan
Jaipur,India
ISSN 2367-3370 ISSN 2367-3389 (electronic)
LectureNotesinNetworksandSystems
ISBN 978-981-19-0178-2 ISBN 978-981-19-0179-9 (eBook)
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Preface
This book is based around the 4th International Conference on “Mathematical
Modelling, Applied Analysis and Computation (ICMMAAC 21)” held in JECRC
University,Jaipuron5–7August2021.Thebookcontainsseveralrecentadvanced
andimportanttopicsinmathematicalmodelling,applicableanalysisandnumerical
simulationshavingusesinscience,engineeringandfinance.Thebookisveryuseful
for the graduate and post-graduate students, researchers and educators working in
differentdirectionsofresearchinappliedmathematicsandrelatedfields.Thegeneral
readersinterestedinmathematicaltheoriesandtechniqueshavingpracticalapplica-
tionsinsolvingreal-worldproblemsshouldalsofindthebookveryinterestingand
useful.Thebookcontains36chapterswhichareorganizedasfollows:
Chapter“ACollectionofHilferFractionalOpialInequalities”presentsacollec-
tion of Hilfer fractional left and right side Opial type inequalities. These cover
forward, reverse and extreme cases, and contain one, two and several functions
of distinct non-integer orders at different powers. The estimates are very general
coveringseveraldistinctsettings.
Chapter “On a Non-linear Diffusion Model of Wood Impregnation: Analysis,
Approximate Solutions, and Experiments with Relaxing Boundary Conditions”
establishes approximate integral-balance solutions of nonlinear diffusion model
for wood impregnation by methacrylate in two cases, namely, Dirichlet boundary
conditionconsideringinstantaneoussaturationofthewoodsurfacecontactingwith
theliquidbathandrelaxingDirichletboundaryconditionsaccountingthefactthat
instantaneoussaturationisunphysicalandtakessometimetobedeveloped.
Chapter “Algorithmic Complexity-Based Fractional-Order Derivatives
in Computational Biology” presents a novel mathematical informed framework
and multi-staged integrative technique concerning algorithmic complexity. This
chapteraimsatinvestigatingarobustandaccuratemodelreliantonthemixtureof
fractional-order derivative and artificial neural network for the diagnostic and
differentiability predictive purposes for the disease which may reveal several and
transient biological characteristic. Another objective of this chapter is benefitting
fromtheconceptofalgorithmiccomplexitytoattainthenon-integerorderderivative
withtheleastcomplexityinorderthatitwouldbepossibletoachievetheoptimized
solution.
v
vi Preface
Chapter “Case Study of Non-singular Kernel Model for MHD Boundary Layer
Flow of a Rate Type Fluid over an Oscillating Plate” presents the MHD boundary
layer flow of rate type fluid over an oscillating inclined infinite plate along with
Newtonianheatingandslipattheboundary.Themodelisestablishedbyapplying
theAtangana-Baleanutime-fractionalderivativeoperator.Temperatureandvelocity
fieldsforthefractional-ordermodelarecalculated.Thephysicalsignificanceofthe
parameters like relaxation time, fractional-order parameter, Grashof number, and
inclinationoftheplateisinvestigatedandtheircontrolonthevelocityofthefluidis
examinedgraphically.
Chapter “Multilayer Perceptron Artificial Neural Network Approach to Solve
Sixth-Order Two-Point Boundary Value Problems” presents a multilayer percep-
tron artificial neural network technique for solving the sixth-order boundary value
problemsthatariseinvariousbranchesofengineeringandphysicssuchashydrody-
namics,fluiddynamics,astrophysics,beamtheoryandsoon.Theobtainedsolutions
of these boundary value problems by applied method are optimal as compared to
otherexistingapproximationtechniques.Inordertodecidetheperformanceofthe
proposedtechniquesomemodelsareanalysed.Thenumericaloutcomesshowthat
the suggested strategy is very effective for higher order boundary value problems
andrequiredlowmemoryspaceandlesscomputationaltime.
Chapter “Wavelet Transform on Generalized Quotient Spaces and Its Appli-
cations” presents the theory of generalized quotients which is a generalization
of Schwartz distributions. The general construction of generalized quotients is
discussed, which is employed to several function spaces in order to attain various
generalized quotient spaces. The wavelet transform is extended to these spaces to
obtain some generalized outcomes. The idea of convolution related to wavelet is
employed to obtain operational properties for quotient of sequences. The wavelet
transformofperiodicquotientofsequencesisexpressedandauniquenesstheorem
isdefinedforthewavelettransformofanalyticfunctions.Somefundamentalconcepts
ofthetheoryofgeneralizedquotientsarediscussedandthensomeofitsapplications
suchasextendingthewavelettransformonaspaceofgeneralizedquotientsonthe
torusareexplained.
Chapter “Certain Image Formulae of the Incomplete I-Function Under
the Conformable and Pathway Fractional Integral and Derivative Operators”
studies several interesting image formulae of the incomplete I-function under the
conformableandpathwayfractionaloperators.SinceboththeincompleteI-function
andtheconformablefractionaloperatorsareverygeneralamongspecialfunctionsas
wellasfractionalintegralandderivativeoperators,theprincipaloutcomesdiscussed
inthischaptercangiveanumberofspecificidentities,someofwhichareexplicitly
showninthecorollaries.
Chapter “Explicit Exact Solutions and Conservation Laws of Modified Alpha
Equation”investigatestheinvariantsolutionsofgeneralizedmodifiedalphaequation
which are derived by utilizing the Lie classical symmetry scheme. The obtained
solutions are in terms of trigonometric functions and hyperbolic functions. This
equationcanbeusedinsolidifyingandnucleationproblem.Theconservationlaws
are obtained by employing the multiplier approach. The graphical representations
Preface vii
are also demonstrated for some of the obtained solutions. Some new solutions of
thoseequationsarefoundthathavebeenconsideredearlierinliterature,aswellas
someoftheprevioussolutionscanalsoberecoveredbyconsideringspecialvalues.
Chapter “Some Approximation Results on Durrmeyer Modification of Gener-
alized Szász–Mirakjan Operators” deals with the approximation features of the
summation-integral-type operators defined by Mishra et al. It consists of the local
outcomesandconvergencetheoremofthedefinedoperators.Theasymptoticnature
of the operators and the quantitative means of Voronovskaja-type theorem are
presented. The Grüss Voronovskaja-type theorem is discussed. To support the
approximationresultsoftheoperators,thegraphicalrepresentationispresented.
Chapter “Fuzzy Approach to Solve General De-Novo Programming Problem”
introduces a modified fuzzy approach to solve GDNPP by means of reflection of
decision-maker’s choice. It is observed that flexibility in decision-maker’s choice
to some extent could be studied in multi-objective linear programming problem
utilizingmeta-goalprogrammingtechnique.Thisflexibilityindecisionprocesscan
alsobeeffectivelyconsideredbyapplyingfuzzyschemeforsolvingGDNPP,which
isobtainedbyintroducingnovelconstraintsasperrequirementoftheproblem.The
proposed technique of solution has been shown by a numerical illustration. The
obtained solutions have been compared with those of other existing techniques of
solvingGDNPP.
Chapter “Comparative Study of Eight Classification Models for Diagnosis
andPredictionofBreastCancer”dealswitheightmodelssuchasLogisticRegres-
sion, K-Nearest Neighbourhood, Decision Tree, Random Forest, Artificial Neural
Network,GaussianNaïveBayes,SupportVectorMachineandAdaBoostclassifier
whichareutilizedforpredictingtwoclasses,i.e.benignandmalignant.Toselectthe
bestfitclassificationmodelforprediction,aconfusionmatrixisusedforevaluating
theperformanceofeachmodel.Further,parameters,forexample,precision,accu-
racy,recall,specificity,F-measureandMatthewscorrelationcoefficient,areinvesti-
gatedforeachmodel.TheWisconsinbreastcancerdiagnosisdatasetandCoimbra
breastcancerdatasetareappliedforexperimentaloutcomes.
Chapter“MathematicalModelforDemonetization”investigatesademonetization
effectonapopulationbyusingacompartmentalmathematicalmodel.Mathematical
analysis of the model presents that there is an existence of demonetization–free
equilibriumanddemonetizationexistenceequilibrium.Thenumericalresultsofthe
modelareobtainedandtheoutcomesrevealthatdemonetizationeffectpersistinthe
system.
Chapter“AnInflationaryDemandSchemewithParetoDeteriorationinTwoWare-
houses”dealswithatwostorageinventorymodel(oneofthemisOwnWarehouse
(OW) and another is Rented Warehouse (RW)) with exponentially time-varying
demand considering partial backlogging. The capacity of own warehouse is fixed
(U units), to store more units than the limited range of OW, the supplier has to
rentanotherwarehouse(RW)athigherholdingcost.Twowarehousepolicieswith
linearholdingcostandPareto–typedecayinaninflationaryenvironmentarestudied.
The sensitivity investigation has been investigated to show the effects of diverse
parametersoftheinventorysystem.
viii Preface
Chapter “Exact Solitary Wave Solutions of the (3+1)-Dimensional Generalised
Kadomtsev-Petviashvili Benjamin-Bona-Mahony Equation” studies the (3+1)-
dimensional generalized Kadomtsev-Petviashvili Benjamin-Bona-Mahony equa-
tion.Byapplyingthemodifiedhyperbolicfunctionexpansionmethod,theexactsoli-
tarywavesolutionsofthenonlinearpartialdifferentialequationhavebeenderived.
The required basic information for the technique of modified hyperbolic expan-
sionhas been provided. Two numerical examples have been demonstrated and the
exactsolutionsobtainedaredescribedwiththehelpoftwo–dimensionalandthree–
dimensionalgraphs.
Chapter“EffectofObliqueMagneticandElectricFieldsontheKelvin-Helmholtz
InstabilityattheInterfaceBetweenPorousandFluidLayers”dealswiththeeffect
ofinclinedmagneticandelectricfieldonthegrowthrateoftheKelvin-Helmholtz
instabilityofaflowinporouslayer.Thebaseflowisconsideredtobefullydeveloped
andthelineartheoriesalongwithnormalmodesareappliedtounderstandthestability
of the flow over the interface between the fluid saturated porous layer and clear
fluidlayeroflargeextent.Theeffectofinclinedmagneticandelectricfieldsonthe
growthrateofinstabilityisexaminedintermsofnon-dimensionalparameters.The
numerical and graphical outcomes demonstrated and validated for wide range of
non-dimensionalparameters.
Chapter“HeatTransferforMHDFlowinanInclinedChannelwithHeatGener-
ation/Absorption” deals with the motion of an incompressible viscous fluid in an
inclined channel. A uniform magnetic field is employed normal to the channel,
considering heat absorption, heat generation and viscous dissipation into account.
The non-dimensional partial differential equations are transformed into ordinary
differentialequations(ODEs)andtheperturbationtechniqueisappliedforsolving
ODEs.Thevelocityandtemperaturepropertieshavebeenanalysedthroughgraphs.
Chapter “Volterra Equation with Constant Fractional Order and Variable Order
Fractal Dimension” studies a general Volterra equation with the new differential
andintegraloperators.Theconditionispresentedunderwhichtheuniquenessand
existence of the exact solutions can be obtained for three cases involving power
law,exponentialdecaylawandthegeneralizedMittag-Lefflerfunction.Numerical
solutionsanderroranalysisarepresentedforeachcase.
Chapter“OntheParabolicInstabilityRegionforKuoProblem”demonstratesKuo
problemwhichdealswithincompressible,inviscid,parallelzonalflows.ForthisKuo
problem,aparabolicinstabilityregionwithoutanyrestrictionwhichintersectswith
Howardsemi-circleundersomeconditionisderived.Anovelupperboundforthe
growthrateofanunstablemodeisobtained.
Chapter “Font Design Through RQT Bézier Curve Using Shape Parameters”
dealswithRQTBéziercurveutilizingtwoshapeparameters.Thesenewcurvesare
more adaptable due to the existence of shape parameters and geometric character-
istics.Toconfirmwhetherthestudiedcurvesatisfiedtheconvexhullcharacteristic
ornot,limitationsonshape,weightanddeclaredend-pointedcurvatureshavebeen
used.Thiscurveisappliedforsmoothcurvecompositionsbygeneratingpiecewise
rationaltrigonometriccurvesthatareadjacentinparametricandgeometricHermite
continuitycriteria.
Preface ix
Chapter “Effect of Partial Slip on Peristaltic Transport of MHD-Carreau Fluid
in a Flexible Channel with Non-uniform Heat Source and Sink” studies the effect
of magnetic field, partial slip flow and irregular heat generation and absorption
of Carreau liquid in peristaltic movement through flexible channel. By using suit-
able non–dimensional parameters the governing equations are reduced to standard
nonlinearpartialdifferentialequations.Byemployingmulti-stepdifferentialtransfor-
mationmethodsolutionsofemergingequationsareobtained.Theroleofinfluential
factorsonvelocity,concentrationandtemperatureisdemonstratedviagraphs.
Chapter “Invariant Preserving Schemes for Multi-symplectic Integrator of Two
LongWaves’Interactions”reportstheideaofdiscreteconservationofsymplecticity
to discretization’s for two long wave’s interactions. This characteristic is endemic
anditisexplainedthatitalsoleadstoexactdiscreteconservationofmomentumand
energyforpropagationtwolongwave’sinteractions.Multi-symplecticintegratorsare
examinedforpropagationtwolongwaves’interactionsandanalysedtheconservation
aspectformulti-symplecticintegrator.Thenumericalsimulationsarealsoshown.
Chapter “Study of Effect of Overlapping Stenosis on Flow Field Considering
Non-Newtonian Reiner Rivlin Blood Flow inArtery” presents the impact of over-
lapping stenosis associate to symmetric stenosis for distinct shape parameters on
parametersofflowfield.ByconsideringReiner–Rivlinstressandstrainconstitutive
relations appropriate for blood rheology the governing conservation equations are
derived.Torevealshearthinning,shearthickeninganddilatancyeffect,thesuitability
ofgeneralizedReiner–Rivlinconstitutiverelationisreportedfromtheliterature.The
solutionforflowfieldisfoundedforsteadyaxi-symmetriccaseforbothoverlapping
stenosisandaxiallysymmetricforseveralshapeparameters.Todiscusstheeffectof
overlapping stenosis associate to symmetric stenosis the flow fields for symmetric
andoverlappingstenosisarecompared.
Chapter“PathwayFractionalIntegralFormulaeInvolvingExtendedBessel-Mait-
landFunctionintheKernel”dealswithtwocompositionformulaeofpathwayfrac-
tionalintegraloperatorsassociatedwithalteredmodificationsoftheBessel-Maitland
function. Pertinent connections of certain special cases of key results with known
outcomeshavebeeninvestigated.
Chapter“AnalyticalApproximateApproachtotheHelmholtz-DuffingOscillator”
studiesanewanalyticalapproximationfortheperiodandperiodicsolutionsforthe
Helmholtz-Duffingoscillator.Thekeyaimofthisworkistoapproximatetheintegra-
tioninexactanalyticalperiodofequationbyapplyingawell-knownquadraturerules.
Comparisonoftheoutcomesattainedemployingthisschemewiththeexactoneand
existingoutcomesshowssimplicity,accuracyandefficiencyoftheproposedmethod
for the whole range of initial amplitudes and the equation parameter in a variety
of cases. The approach can be easily modified to other existing strongly nonlinear
oscillators.
Chapter “Haar Wavelet Series Method for Solving Simultaneous Proportional
DelayDifferentialEquations”reportsanovelnumericaltechniquetofindtheapprox-
imatesolutionofsimultaneousproportionaldelaydifferentialequations(SPDDEs).
TotransformtheSPDDEsintoasystemofalgebraicmatrixequationswithunknown
coefficients matrices, the discussed method uses delayed Haar wavelet series and
collocation points. By applying suitable solver, the values of these unknown row
