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EBOOK
Author Annaby, Mahmoud H.
Title Q-fractional calculus and equations / Mahmoud H. Annaby, Zeinab S. Mansour.
Imprint Berlin ; New York : Springer, 2012.

LOCATION CALL # STATUS MESSAGE
 OHIOLINK SPRINGER EBOOKS    ONLINE  
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Author Annaby, Mahmoud H.
Series Lecture notes in mathematics, 0075-8434 ; 2056
Lecture notes in mathematics (Springer-Verlag) ; 2056.
Subject Fractional calculus.
Alt Name Mansour, Zeinab S.
LOCATION CALL # STATUS MESSAGE
 OHIOLINK SPRINGER EBOOKS    ONLINE  
View online
Author Annaby, Mahmoud H.
Series Lecture notes in mathematics, 0075-8434 ; 2056
Lecture notes in mathematics (Springer-Verlag) ; 2056.
Subject Fractional calculus.
Alt Name Mansour, Zeinab S.
Description 1 online resource.
Contents 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 -- q-Integral Transforms for Solving Fractional q-Difference Equations.
Bibliography Note Includes bibliographical references and index.
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; Grunwald-Letnikov; Caputo; Erdelyi-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.
Note English.
ISBN 9783642308987 (electronic bk.)
3642308988 (electronic bk.)
364230897X
9783642308970
9783642308970
ISBN/ISSN 10.1007/978-3-642-30898-7
OCLC # 809202760
Additional Format Printed edition: 9783642308970



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