q-Fractional calculus and equations
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 der...
Shranjeno v:
| Auteurs principaux: | , |
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| Format: | Livre numérique |
| Jezik: | Anglais |
| Izdano: |
Berlin, Heidelberg :
Springer Berlin Heidelberg
[20..].
Cham : Springer Nature |
| Izdaja: | 1st ed. 2012. |
| Serija: | Lecture notes in mathematics
2056 |
| Teme: | |
| Online dostop: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Sporočilo: |
L'impression du document génère 332 p. Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • q-Fractional calculus and equations, Mahmoud H. Annaby, Zeinab S. Mansour, Heidelberg, Springer Verlag, 2012, 1 vol. (xix-318 p.), Lecture notes in mathematics, 978-3-642-30897-0 • q-Fractional calculus and equations, Mahmoud H. Annaby, Zeinab S. Mansour, Heidelberg, Springer Verlag, 2012, 1 vol. (xix-318 p.), Lecture notes in mathematics, 978-3-642-30897-0 • q-Fractional Calculus and Equations, Texte imprimé, 9783642308994 |
| Izvleček: | 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 |
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| Opis knjige/članka: | L'impression du document génère 332 p. Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Bibliografija: | Bibliogr. Index |
| ISBN: | 9783642308987 |
| ISSN: | 1617-9692 |
| Dostop: | Accès en ligne pour les établissements français bénéficiaires des licences nationales Accès soumis à abonnement pour tout autre établissement Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 |