The Resource Qfractional calculus and equations, Mahmoud H. Annaby, Zeinab S. Mansour
Qfractional calculus and equations, Mahmoud H. Annaby, Zeinab S. Mansour
Resource Information
The item Qfractional calculus and equations, Mahmoud H. Annaby, Zeinab S. Mansour represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.This item is available to borrow from 1 library branch.
Resource Information
The item Qfractional calculus and equations, Mahmoud H. Annaby, Zeinab S. Mansour represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.
This item is available to borrow from 1 library branch.
 Summary
 This ninechapter monograph introduces a rigorous investigation of qdifference operators in standard and fractional settings. It starts with elementary calculus of qdifferences and integration of Jackson's type before turning to qdifference equations. The existence and uniqueness theorems are derived using successive approximations, leading to systems of equations with retarded arguments. Regular qSturmLiouville theory is also introduced; Green's function is constructed and the eigenfunction expansion theorem is given. The monograph also discusses some integral equations of Volterra and Abel type, as introductory material for the study of fractional qcalculi. Hence fractional qcalculi of the types RiemannLiouville; GrünwaldLetnikov; Caputo; ErdélyiKober and Weyl are defined analytically. Fractional qLeibniz rules with applications in qseries are also obtained with rigorous proofs of the formal results of AlSalamVerma, which remained unproved for decades. In working towards the investigation of qfractional difference equations; families of qMittagLeffler functions are defined and their properties are investigated, especially the qMellinBarnes integral and Hankel contour integral representation of the qMittagLeffler functions under consideration, the distribution, asymptotic and reality of their zeros, establishing qcounterparts of Wiman's results. Fractional qdifference equations are studied; existence and uniqueness theorems are given and classes of Cauchytype problems are completely solved in terms of families of qMittagLeffler functions. Among many qanalogs of classical results and concepts, qLaplace, qMellin and q2Fourier transforms are studied and their applications are investigated
 Language
 eng
 Extent
 1 online resource.
 Contents

 qIntegral Transforms for Solving Fractional qDifference Equations
 Preliminaries
 qDifference Equations
 qSturmLiouville Problems
 RiemannLiouville qFractional Calculi
 Other qFractional Calculi
 Fractional qLeibniz Rule and Applications
 qMittagLeffler Functions
 Fractional qDifference Equations
 Isbn
 9783642308970
 Label
 Qfractional calculus and equations
 Title
 Qfractional calculus and equations
 Statement of responsibility
 Mahmoud H. Annaby, Zeinab S. Mansour
 Language
 eng
 Summary
 This ninechapter monograph introduces a rigorous investigation of qdifference operators in standard and fractional settings. It starts with elementary calculus of qdifferences and integration of Jackson's type before turning to qdifference equations. The existence and uniqueness theorems are derived using successive approximations, leading to systems of equations with retarded arguments. Regular qSturmLiouville theory is also introduced; Green's function is constructed and the eigenfunction expansion theorem is given. The monograph also discusses some integral equations of Volterra and Abel type, as introductory material for the study of fractional qcalculi. Hence fractional qcalculi of the types RiemannLiouville; GrünwaldLetnikov; Caputo; ErdélyiKober and Weyl are defined analytically. Fractional qLeibniz rules with applications in qseries are also obtained with rigorous proofs of the formal results of AlSalamVerma, which remained unproved for decades. In working towards the investigation of qfractional difference equations; families of qMittagLeffler functions are defined and their properties are investigated, especially the qMellinBarnes integral and Hankel contour integral representation of the qMittagLeffler functions under consideration, the distribution, asymptotic and reality of their zeros, establishing qcounterparts of Wiman's results. Fractional qdifference equations are studied; existence and uniqueness theorems are given and classes of Cauchytype problems are completely solved in terms of families of qMittagLeffler functions. Among many qanalogs of classical results and concepts, qLaplace, qMellin and q2Fourier transforms are studied and their applications are investigated
 Cataloging source
 GW5XE
 http://library.link/vocab/creatorName
 Annaby, Mahmoud H
 Dewey number
 515/.83
 Index
 index present
 Language note
 English
 LC call number
 QA314
 LC item number
 .A56 2012
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 http://library.link/vocab/relatedWorkOrContributorName
 Mansour, Zeinab S
 Series statement
 Lecture notes in mathematics,
 Series volume
 2056
 http://library.link/vocab/subjectName

 Fractional calculus
 Fractional calculus
 Label
 Qfractional calculus and equations, Mahmoud H. Annaby, Zeinab S. Mansour
 Antecedent source
 unknown
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents

 qIntegral Transforms for Solving Fractional qDifference Equations
 Preliminaries
 qDifference Equations
 qSturmLiouville Problems
 RiemannLiouville qFractional Calculi
 Other qFractional Calculi
 Fractional qLeibniz Rule and Applications
 qMittagLeffler Functions
 Fractional qDifference Equations
 Control code
 809202760
 Dimensions
 unknown
 Extent
 1 online resource.
 File format
 unknown
 Form of item
 online
 Isbn
 9783642308970
 Level of compression
 unknown
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/9783642308987
 Quality assurance targets
 not applicable
 Reformatting quality
 unknown
 Sound
 unknown sound
 Specific material designation
 remote
 System control number
 (OCoLC)809202760
 Label
 Qfractional calculus and equations, Mahmoud H. Annaby, Zeinab S. Mansour
 Antecedent source
 unknown
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents

 qIntegral Transforms for Solving Fractional qDifference Equations
 Preliminaries
 qDifference Equations
 qSturmLiouville Problems
 RiemannLiouville qFractional Calculi
 Other qFractional Calculi
 Fractional qLeibniz Rule and Applications
 qMittagLeffler Functions
 Fractional qDifference Equations
 Control code
 809202760
 Dimensions
 unknown
 Extent
 1 online resource.
 File format
 unknown
 Form of item
 online
 Isbn
 9783642308970
 Level of compression
 unknown
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/9783642308987
 Quality assurance targets
 not applicable
 Reformatting quality
 unknown
 Sound
 unknown sound
 Specific material designation
 remote
 System control number
 (OCoLC)809202760
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.library.missouri.edu/portal/QfractionalcalculusandequationsMahmoudH./qkf1TupuccE/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.missouri.edu/portal/QfractionalcalculusandequationsMahmoudH./qkf1TupuccE/">Qfractional calculus and equations, Mahmoud H. Annaby, Zeinab S. Mansour</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.missouri.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.missouri.edu/">University of Missouri Libraries</a></span></span></span></span></div>