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035   $a(DE-He213)978-3-642-30898-7
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100   $a20120730d2012      uy         0
101 0 $aeng
135   $aurnn#008mamaa
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aq-Fractional calculus and equations /$fMahmoud H. Annaby, Zeinab S. Mansour
205   $a1st ed. 2012.
210   $aBerlin ;$aHeidelberg $cSpringer$dc2012
215   $a1 online resource (xix, 318 pages) $cillustrations
225 1 $aLecture notes in mathematics,$x0075-8434 ;$v2056
311   $a3-642-30897-X 
320   $aIncludes bibliographical references (p. 303-314) and indexes.
327   $a1 Preliminaries -- 2 q-Difference Equations -- 3 q-Sturm Liouville Problems -- 4 Riemann?Liouville q-Fractional Calculi -- 5 Other q-Fractional Calculi -- 6 Fractional q-Leibniz Rule and Applications -- 7 q-Mittag?Leffler Functions -- 8 Fractional q-Difference Equations -- 9 Applications of q-Integral Transforms.
330   $aThis nine-chapter monograph introduces a rigorous investigation of q-difference operators in standard and fractional settings. It starts with elementary calculus of q-differences and integration of Jackson?s type before turning to q-difference equations. The existence and uniqueness theorems are derived using successive approximations, leading to systems of equations with retarded arguments. Regular  q-Sturm?Liouville theory is also introduced; Green?s function is constructed and the eigenfunction expansion theorem is given. The monograph also discusses some integral equations of Volterra and Abel type, as introductory material for the study of fractional q-calculi. Hence fractional q-calculi of the types Riemann?Liouville; Grünwald?Letnikov;  Caputo;  Erdélyi?Kober and Weyl are defined analytically. Fractional q-Leibniz rules with applications  in q-series are  also obtained with rigorous proofs of the formal  results of  Al-Salam-Verma, which remained unproved for decades. In working towards the investigation of q-fractional difference equations; families of q-Mittag-Leffler functions are defined and their properties are investigated, especially the q-Mellin?Barnes integral  and Hankel contour integral representation of  the q-Mittag-Leffler functions under consideration,  the distribution, asymptotic and reality of their zeros, establishing q-counterparts of Wiman?s results. Fractional q-difference equations are studied; existence and uniqueness theorems are given and classes of Cauchy-type problems are completely solved in terms of families of q-Mittag-Leffler functions. Among many q-analogs of classical results and concepts, q-Laplace, q-Mellin and q2-Fourier transforms are studied and their applications are investigated.
410  0$aLecture notes in mathematics (Springer-Verlag) ;$v2056.
606   $aFractional calculus
606   $aDifference equations
615  0$aFractional calculus.
615  0$aDifference equations.
676   $a515.83
700   $aAnnaby$b Mahmoud H$0477683
701   $aMansour$b Zeinab S$0518042
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910484622003321
996   $aQ-fractional calculus and equations$9848040
997   $aUNINA