Coverart for item
The Resource Q-fractional calculus and equations, Mahmoud H. Annaby, Zeinab S. Mansour

Q-fractional calculus and equations, Mahmoud H. Annaby, Zeinab S. Mansour

Label
Q-fractional calculus and equations
Title
Q-fractional calculus and equations
Statement of responsibility
Mahmoud H. Annaby, Zeinab S. Mansour
Creator
Contributor
Subject
Language
eng
Summary
This nine-chapter monograph introduces a rigorous investigation of q-difference operators in standard and fractional settings. It starts with elementary calculus of q-differences and integration of Jackson's type before turning to q-difference equations. The existence and uniqueness theorems are derived using successive approximations, leading to systems of equations with retarded arguments. Regular q-Sturm-Liouville 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 q-calculi. Hence fractional q-calculi of the types Riemann-Liouville; Grünwald-Letnikov; Caputo; Erdélyi-Kober and Weyl are defined analytically. Fractional q-Leibniz rules with applications in q-series are also obtained with rigorous proofs of the formal results of Al-Salam-Verma, which remained unproved for decades. In working towards the investigation of q-fractional difference equations; families of q-Mittag-Leffler functions are defined and their properties are investigated, especially the q-Mellin-Barnes integral and Hankel contour integral representation of the q-Mittag-Leffler functions under consideration, the distribution, asymptotic and reality of their zeros, establishing q-counterparts of Wiman's results. Fractional q-difference equations are studied; existence and uniqueness theorems are given and classes of Cauchy-type problems are completely solved in terms of families of q-Mittag-Leffler functions. Among many q-analogs of classical results and concepts, q-Laplace, q-Mellin and q2-Fourier transforms are studied and their applications are investigated
Member of
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
Q-fractional calculus and equations, Mahmoud H. Annaby, Zeinab S. Mansour
Instantiates
Publication
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
  • q-Integral Transforms for Solving Fractional q-Difference Equations
  • Preliminaries
  • q-Difference Equations
  • q-Sturm-Liouville Problems
  • Riemann-Liouville q-Fractional Calculi
  • Other q-Fractional Calculi
  • Fractional q-Leibniz Rule and Applications
  • q-Mittag-Leffler Functions
  • Fractional q-Difference 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
10.1007/978-3-642-30898-7
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
(OCoLC)809202760
Label
Q-fractional calculus and equations, Mahmoud H. Annaby, Zeinab S. Mansour
Publication
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
  • q-Integral Transforms for Solving Fractional q-Difference Equations
  • Preliminaries
  • q-Difference Equations
  • q-Sturm-Liouville Problems
  • Riemann-Liouville q-Fractional Calculi
  • Other q-Fractional Calculi
  • Fractional q-Leibniz Rule and Applications
  • q-Mittag-Leffler Functions
  • Fractional q-Difference 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
10.1007/978-3-642-30898-7
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
(OCoLC)809202760

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