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...
Kaydedildi:
| Asıl Yazarlar: | , |
|---|---|
| Materyal Türü: | Livre numérique |
| Dil: | Anglais |
| Baskı/Yayın Bilgisi: |
Berlin, Heidelberg :
Springer Berlin Heidelberg
[20..].
Cham : Springer Nature |
| Edisyon: | 1st ed. 2012. |
| Seri Bilgileri: | Lecture notes in mathematics
2056 |
| Konular: | |
| Online Erişim: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Not: |
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 |
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| 084 | |a 33D15. 2010 | ||
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| 100 | 1 | |a Annaby, Mahmoud H., |d 19..- | |
| 245 | 1 | 0 | |a q-Fractional calculus and equations |c Mahmoud H. Annaby, Zeinab S. Mansour. |
| 250 | |a 1st ed. 2012. | ||
| 260 | |a Berlin, Heidelberg : |b Springer Berlin Heidelberg. | ||
| 260 | |a Cham : |b Springer Nature, |c [20..]. | ||
| 490 | 1 | |a Lecture notes in mathematics |v 2056 |x 1617-9692 | |
| 500 | |a L'impression du document génère 332 p. | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 504 | |a Bibliogr. Index | ||
| 505 | 1 | |a 1 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 | |
| 506 | |a Accès en ligne pour les établissements français bénéficiaires des licences nationales | ||
| 506 | |a Accès soumis à abonnement pour tout autre établissement | ||
| 506 | |a Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 | ||
| 520 | |a 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 | ||
| 650 | |a Équations aux différences | ||
| 700 | 1 | |a Mansour, Zeinab S., |d 19..- |4 aut | |
| 776 | 0 | |0 164622128 |t q-Fractional calculus and equations |f Mahmoud H. Annaby, Zeinab S. Mansour |c Heidelberg |n Springer Verlag |d 2012 |p 1 vol. (xix-318 p.) |s Lecture notes in mathematics |z 978-3-642-30897-0 | |
| 776 | 0 | |0 164622128 |t q-Fractional calculus and equations |f Mahmoud H. Annaby, Zeinab S. Mansour |c Heidelberg |n Springer Verlag |d 2012 |p 1 vol. (xix-318 p.) |s Lecture notes in mathematics |z 978-3-642-30897-0 | |
| 776 | 0 | |t q-Fractional Calculus and Equations |b Texte imprimé |z 9783642308994 | |
| 856 | 4 | |q PDF |u https://doi.org/10.1007/978-3-642-30898-7 |z Accès sur la plateforme de l'éditeur | |
| 856 | 4 | |u https://revue-sommaire.istex.fr/ark:/67375/8Q1-FQ5HN9B3-8 |z Accès sur la plateforme Istex | |
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