000 | 04620nam a22005775i 4500 | ||
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001 | 978-3-642-30898-7 | ||
003 | DE-He213 | ||
005 | 20190213151307.0 | ||
007 | cr nn 008mamaa | ||
008 | 120825s2012 gw | s |||| 0|eng d | ||
020 |
_a9783642308987 _9978-3-642-30898-7 |
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_a10.1007/978-3-642-30898-7 _2doi |
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_aPBK _2bicssc |
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_aMAT034000 _2bisacsh |
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_aPBK _2thema |
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_a515 _223 |
100 | 1 |
_aAnnaby, Mahmoud H. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut |
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245 | 1 | 0 |
_aq -Fractional Calculus and Equations _h[electronic resource] / _cby Mahmoud H. Annaby, Zeinab S. Mansour. |
264 | 1 |
_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg : _bImprint: Springer, _c2012. |
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300 |
_aXIX, 318 p. 6 illus. _bonline resource. |
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336 |
_atext _btxt _2rdacontent |
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337 |
_acomputer _bc _2rdamedia |
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338 |
_aonline resource _bcr _2rdacarrier |
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347 |
_atext file _bPDF _2rda |
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490 | 1 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v2056 |
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505 | 0 | _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. | |
520 | _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. | ||
650 | 0 | _aGlobal analysis (Mathematics). | |
650 | 0 | _aFunctional equations. | |
650 | 0 | _aFunctions of complex variables. | |
650 | 0 | _aIntegral Transforms. | |
650 | 0 | _aIntegral equations. | |
650 | 0 | _aMathematical physics. | |
650 | 1 | 4 |
_aAnalysis. _0http://scigraph.springernature.com/things/product-market-codes/M12007 |
650 | 2 | 4 |
_aDifference and Functional Equations. _0http://scigraph.springernature.com/things/product-market-codes/M12031 |
650 | 2 | 4 |
_aFunctions of a Complex Variable. _0http://scigraph.springernature.com/things/product-market-codes/M12074 |
650 | 2 | 4 |
_aIntegral Transforms, Operational Calculus. _0http://scigraph.springernature.com/things/product-market-codes/M12112 |
650 | 2 | 4 |
_aIntegral Equations. _0http://scigraph.springernature.com/things/product-market-codes/M12090 |
650 | 2 | 4 |
_aMathematical Methods in Physics. _0http://scigraph.springernature.com/things/product-market-codes/P19013 |
700 | 1 |
_aMansour, Zeinab S. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut |
|
710 | 2 | _aSpringerLink (Online service) | |
773 | 0 | _tSpringer eBooks | |
776 | 0 | 8 |
_iPrinted edition: _z9783642308970 |
776 | 0 | 8 |
_iPrinted edition: _z9783642308994 |
830 | 0 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v2056 |
|
856 | 4 | 0 | _uhttps://doi.org/10.1007/978-3-642-30898-7 |
912 | _aZDB-2-SMA | ||
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