Advances in Real and Complex Analysis with Applications

304 Pages·2017·3.995 MB·English

by  Michael Ruzhansky,Yeol Je Cho,Praveen Agarwal,Iván Area (eds.)

Trends in Mathematics
Michael Ruzhansky
Yeol Je Cho
Praveen Agarwal
Iván Area
Editors
Advances
in Real and
Complex
Analysis with
Applications

Trends in Mathematics
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Michael Ruzhansky Yeol Je Cho
(cid:129)
á
Praveen Agarwal Iv n Area
(cid:129)
Editors
Advances in Real
and Complex Analysis
with Applications
Editors
Michael Ruzhansky Praveen Agarwal
Department ofMathematics Department ofMathematics
Imperial CollegeLondon Anand International Collegeof Engineering
London Jaipur,Rajasthan
UK India
YeolJe Cho Iván Area
Department ofMathematics Education Departamento deMatemática AplicadaII
andtheRINS E.E.AeronáuticaedoEspazo,Universidade
Gyeonsang National University deVigo
Jinju Ourense
Korea (Republicof) Spain
ISSN 2297-0215 ISSN 2297-024X (electronic)
Trends inMathematics
ISBN978-981-10-4336-9 ISBN978-981-10-4337-6 (eBook)
DOI 10.1007/978-981-10-4337-6
LibraryofCongressControlNumber:2017945222
MathematicsSubjectClassification(2010):11A15,30C45,42A38,44A10,46G20,46E50
©SpringerNatureSingaporePteLtd.2017
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Contents
Certain Image Formulae and Fractional Kinetic Equations
Involving Extended Hypergeometric Functions.... .... .... ..... .... 1
Krunal B. Kachhia, Praveen Agarwal and Jyotindra C. Prajapati
The Compact Approximation Property for Weighted Spaces
of Holomorphic Mappings ... ..... .... .... .... .... .... ..... .... 33
Manjul Gupta and Deepika Baweja
Bloch Mappings on Bounded Symmetric Domains. .... .... ..... .... 49
Tatsuhiro Honda
Certain Class of Meromorphically Multivalent Functions
Defined by a Differential Operator . .... .... .... .... .... ..... .... 71
Ghazi S. Khammash and Praveen Agarwal
Bivariate Symmetric Discrete Orthogonal Polynomials . .... ..... .... 87
Y. Guemo Tefo, Iván Area and M. Foupouagnigni
New and Extended Applications of the Natural and Sumudu
Transforms: Fractional Diffusion and Stokes Fluid Flow Realms.. .... 107
Fethi Bin Muhammed Belgacem, Rathinavel Silambarasan,
Hammouch Zakia and Toufik Mekkaoui
On Uncertain-Fractional Modeling: The Future Way
of Modeling Real-World Problems . .... .... .... .... .... ..... .... 121
Abdon Atangana and Ilknur Koca
Quadratic Reciprocity and Some “Non-differentiable” Functions.. .... 145
Kalyan Chakraborty and Azizul Hoque
Survey on Metric Fixed Point Theory and Applications .... ..... .... 183
Yeol Je Cho
Sums of Finite Products of Euler Functions . .... .... .... ..... .... 243
Taekyun Kim, Dae San Kim, Gwan Woo Jang and Jongkyum Kwon
v
vi Contents
On a New Extension of Caputo Fractional Derivative Operator .. .... 261
İ.O. Kıymaz, P. Agarwal, S. Jain and A. Çetinkaya
An Extension of the Shannon Wavelets for Numerical Solution
of Integro-Differential Equations... .... .... .... .... .... ..... .... 277
Maryam Attary
Inverse Source Problem for Multi-term Fractional Mixed
Type Equation. .... .... .... ..... .... .... .... .... .... ..... .... 289
E.T. Karimov, S. Kerbal and N. Al-Salti
About the Editors
Michael Ruzhansky is a Professor at the Department of Mathematics, Imperial
College London. He has published over 100 research articles in several leading
international journals. He has also published five books and memoirs and nine
edited volumes. He has researched topics related to pseudo-differential operators,
harmonicanalysis,andpartialdifferential equations. Morerecently,hehasworked
on boundary value problems and their applications. He has been on the editorial
board of many respected international journals and served as the President of the
International Society of Analysis, Applications, and Computations (ISAAC) in the
period 2009–2013.
Yeol Je Cho is a Professor at the Department of Mathematics Education,
Gyeongsang National University, Korea, and Fellow of the Korean Academy of
Science and Technology. He has published over 350 research papers in respected
internationaljournals,mainlyinthefieldoffixedpointtheory,variationalinequality
problems, equilibrium problems, optimization problems, stability of functional
equations, and inequality theory. He has been on the editorial boards of several
leadingjournals,suchasFixedPointTheoryandApplications,JournalofNonlinear
Science and Applications, and 15 more international journal of mathematics and
applications. He has also published a number of remarkable books on fixed point
theory,stability offunctional equations,numerical analysis, and degree theory.
Praveen Agarwal is a Professor at the Department of Mathematics, Anand
International College of Engineering, Jaipur, India. He has published over 150
articles related to special functions and fractional calculus in leading mathematics
journals,suchasAppliedMathematicsandComputation,theJournalofNonlinear
Science and Applications, and the Journal of Inequalities and Applications.
Recently, hehas focused on partial differential equationsand fractional differential
equations. He has been on the editorial boards of several journals, including
SpringerPlus and the Maejo International Journal of Science and Technology. He
has been involved in a number of conferences and has also won numerous
vii
viii AbouttheEditors
internationalresearchgrantssuchasResearchinGroupbyInternationalCentrefor
MathematicalSciences(ICMS)andWorldAcademyofSciences(TWAS)Visiting
Scientist fellowship and many more.
Iván Area is a Professor at the Departamento de Matemática Aplicada II,
E.E.AeronáuticaedoEspazoUniversidadedeVigo,Spain.Hehaspublishedover
100 articles related to orthogonal polynomials and special functions in leading
internationaljournals.Hisrecentresearchhasalsofocusedonfractionalanalysisand
bioinformatics.HehasbeenelectedGeneralSecretaryoftheInternationalCenterfor
PureandAppliedMathematics(CIMPA),anonprofitorganizationwhoseaimisto
promotemathematics in developing countries.
Certain Image Formulae and Fractional
Kinetic Equations Involving Extended
Hypergeometric Functions
KrunalB.Kachhia,PraveenAgarwalandJyotindraC.Prajapati
Abstract In this chapter, our aim is to establish certain new image formulae of
generalizedhypergeometricfunctionsbyusingtheoperatorsoffractionalcalculus.
Some new image formulae are obtained by applying specific integral transforms
on resulting image formulae. We also acquired generalization of fractional kinetic
equationsinvolvingextendedhypergeometricfunctions.
·
Keywords Generalized Gauss hypergeometric function Fractional derivative
· · ·
operators Integraltransforms Fractionalkineticequation Mittag–Lefflerfunction
· · · ·
2010 AMS Math. Subject Classification 26A33 33B15 33C15 33C20
· ·
33C99 44A10 33E20
1 Introduction
Fractionalcalculusisoneofthegeneralizationsofclassicalcalculus,andithasbeen
usedsuccessfullyinvariousfieldsofscienceandtechnology.Manyapplicationsof
fractional calculus can be found in other diverse fields, etc. (See [15, 17, 19–22,
35]).
Integraltransformsandfractionalintegralformulaeinvolvingwell-knownspecial
functions are interesting in themselves and play significant roles in their diverse
K.B.Kachhia
FacultyofAppliedSciences,DepartmentofMathematicalSciences,Charotar
UniversityofScienceandTechnology(CHARUSAT),Changa388421,Gujarat,India
e-mail:[email protected]
B
P.Agarwal( )
DepartmentofMathematics,AnandInternationalCollegeofEngineering,Jaipur303012,
Rajasthan,India
e-mail:[email protected]
J.C.Prajapati
DepartmentofMathematics,MarwadiUniversity,Rajkot-MorbiRoad,Rajkot360003,
Gujarat,India
e-mail:[email protected]
©SpringerNatureSingaporePteLtd.2017 1
M.Ruzhanskyetal.(eds.),AdvancesinRealandComplexAnalysis
withApplications,TrendsinMathematics,DOI10.1007/978-981-10-4337-6_1