Table Of ContentNonlinear Systems and Complexity 23
Series Editor: Albert C. J. Luo
Kenan Taş · Dumitru Baleanu
J. A. Tenreiro Machado Editors
Mathematical
Methods in
Engineering
Theoretical Aspects
Nonlinear Systems and Complexity
Volume 23
Serieseditor
AlbertC.J.Luo
SouthernIllinoisUniversity
Edwardsville,IL,USA
Nonlinear Systems and Complexity providesa place to systematically summarize
recentdevelopments,applications,andoveralladvanceinallaspectsofnonlinearity,
chaos,andcomplexityaspartoftheestablishedresearchliterature,beyondthenovel
andrecentfindingspublishedinprimaryjournals.Theaimsofthe bookseriesare
to publishtheoriesandtechniquesin nonlinearsystems andcomplexity;stimulate
moreresearchinterestonnonlinearity,synchronization,andcomplexityinnonlinear
science; and fast-scatter the new knowledge to scientists, engineers, and students
in the correspondingfields. Books in this series will focus on the recent develop-
ments, findings and progress on theories, principles, methodology, computational
techniques in nonlinear systems and mathematics with engineering applications.
TheSeriesestablisheshighlyrelevantmonographsonwiderangingtopicscovering
fundamental advances and new applications in the field. Topical areas include,
but are not limited to: Nonlinear dynamics Complexity, nonlinearity, and chaos
Computational methods for nonlinear systems Stability, bifurcation, chaos and
fractals in engineering Nonlinear chemical and biological phenomena Fractional
dynamicsandapplicationsDiscontinuity,synchronizationandcontrol.
Moreinformationaboutthisseriesathttp://www.springer.com/series/11433
Kenan Tas¸ • Dumitru Baleanu
J. A. Tenreiro Machado
Editors
Mathematical Methods
in Engineering
Theoretical Aspects
123
Editors
KenanTas¸ DumitruBaleanu
DepartmentofMathematics DepartmentofMathematics
ÇankayaUniversity ÇankayaUniversity
Ankara,Turkey Ankara,Turkey
J.A.TenreiroMachado
InstitutoSuperiordeEngenhariadoPorto
Porto,Portugal
ISSN2195-9994 ISSN2196-0003 (electronic)
NonlinearSystemsandComplexity
ISBN978-3-319-91064-2 ISBN978-3-319-91065-9 (eBook)
https://doi.org/10.1007/978-3-319-91065-9
LibraryofCongressControlNumber:2018951218
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Preface
This work, organized into two volumes, publishes a selection of most relevant
contributions,presentedattheInternationalSymposium,MME2017Mathematical
MethodsinEngineering,heldatÇankayaUniversity,Ankara,Turkey,duringApril
27–29,2017.
ThefirstvolumeofthebookMathematicalMethodsinEngineering-Theoretical
Aspects”isdividedintotwoparts,namely,“Fixedpointtheoryandapplications”and
“Newmathematicalideas.”
The reader starts by finding an excellent review about the fixed point results
on partial metric spaces. This book also includes 13 high-quality contributions.
The book expands the works entitled: Fixed points results for mixed multivalued
mappings of Feng-Liu type on Mb-metric spaces, Hyers-Ulam and Hyers-Ulam-
Rassias stability for a class of integro-differentialequations, Exact solutions, Lie
symmetryanalysisandconservationlawsofthetimefractionaldiffusion-absorption
equation,Integralbalanceapproachto 1-Dspace-fractionalmodels:approximate
solutions and analysis, Fractional order filter discretization by particle swarm
optimization method, and On the existence of solution for a sum fractional finite
differenceinclusion.
In addition, the book contains Comparison on solving a class of nonlinear
systems of partial differential equations and multiple solutions of second order
differential equations, Effect of edge deletion and addition on Zagreb indices of
graphs,ThelimitQ-BernsteinoperatorswithvaryingQ,Localizationofthespectral
expansions associated with the partial differential operators, Energy decay in a
quasilinearsystemwithfiniteandinfinitememories,Anewmethodforsolvingtwo-
dimensionalBratudifferentialequation,andAnoteontheupperboundofaverage
distanceviairregularityindex.
The symposium provided a forum for discussing recent developments about
theoreticalandappliedareasofmathematicsandengineeringwithemphasisonthe
topicsfractionalcalculusandnonlinearanalysis.
The members of the organizing committee were Kenan Tas¸ (Turkey), J. A.
TenreiroMachado(Portugal),andYangjianCai(China).
v
vi Preface
All local organizing committee members with leadership of Dumitru Baleanu
and all members of Çankaya University, Mathematics Department, as well as the
organizers of Special Sessions, Plenary and Invited Speakers, and International
ScientificCommitteedeserveheartfeltthanks.
TheeditorsofthisbookaregratefultothePresidentoftheboardoftrusteesof
ÇankayaUniversity,SitkiAlp,andtotheRector,Prof.Dr.HamdiMollamahmuto-
glu,fortheircontinuoussupportofthesymposiumactivities.
We would like to thank all the referees and other colleagues who helped in
preparingthisbookforpublication.
Finally,ourspecialthanksareduetoKiruthikaKumarandMichaelLubyfrom
Springer,fortheircontinuoushelpandworkinconnectionwiththisbook.
Ankara,Turkey KenanTas¸
Ankara,Turkey DumitruBaleanu
Porto,Portugal J.A.TenreiroMachado
Contents
PartI FixedPointTheoryandApplications
1 AdvancesonFixedPointResultsonPartialMetricSpaces............ 3
ErdalKarapınar,KenanTas¸,andVladimirRakocˇevic´
2 FixedPoint Results for Mixed Multivalued Mappings of
Feng-LiuTypeonM -MetricSpaces..................................... 67
b
HakanS¸ahin,IshakAltun,andDuranTürkog˘lu
3 Hyers-UlamandHyers-Ulam-RassiasStabilityforaClassof
Integro-DifferentialEquations............................................ 81
L.P.CastroandA.M.Simões
PartII NewMathematicalIdeas
4 ExactSolutions,LieSymmetryAnalysisandConservation
LawsoftheTimeFractionalDiffusion-AbsorptionEquation......... 97
MirSajjadHashemi,ZahraBalmeh,andDumitruBaleanu
5 IntegralBalanceApproachto1-DSpace-FractionalDiffusion
Models ....................................................................... 111
JordanHristov
6 FractionalOrder FilterDiscretizationby ParticleSwarm
OptimizationMethod ...................................................... 133
Ozlem Imik, Baris Baykant Alagoz, Abdullah Ates,
andCelaleddinYeroglu
7 Onthe Existence ofSolutionfor a Sum FractionalFinite
DifferenceInclusion........................................................ 145
VahidGhorbanian,ShahramRezapour,andSaeidSalehi
vii
viii Contents
8 ComparisononSolvingaClassofNonlinearSystemsofPartial
DifferentialEquationsandMultipleSolutionsofSecondOrder
DifferentialEquations...................................................... 161
AliAkgül,EsraKaratasAkgül,YasirKhan,andDumitruBaleanu
9 EffectofEdgeDeletionandAdditiononZagrebIndicesofGraphs.. 191
MugeTogan,AysunYurttas,AhmetSinanCevik,
andIsmailNaciCangul
10 TheLimitq-BernsteinOperatorswithVaryingq ...................... 203
ManalMastafaAlmesbahi,SofiyaOstrovska,andMehmetTuran
11 LocalizationoftheSpectralExpansionsAssociatedwiththe
PartialDifferentialOperators............................................. 217
AbdumalikRakhimov
12 EnergyDecayinaQuasilinearSystemwithFiniteandInfinite
Memories.................................................................... 235
MuhammadI.Mustafa
13 AModifiedandEnhancedAntColonyOptimizationAlgorithm
forTravelingSalesmanProblem.......................................... 257
LeilaEskandari,AhmadJafarian,ParastooRahimloo,
andDumitruBaleanu
14 A Note on the Upper Bound of Average Distance via
IrregularityIndex .......................................................... 267
NihatAkgunes,IsmailNaciCangul,andAhmetSinanCevik
Index............................................................................... 273
Part I
Fixed Point Theory and Applications
