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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 ar...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , |
| Autor Corporativo: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Berlin, Heidelberg :
Springer Berlin Heidelberg : Imprint: Springer,
2012.
|
| Edición: | 1st ed. 2012. |
| Colección: | Lecture Notes in Mathematics,
2056 |
| Temas: | |
| Acceso en línea: | Texto Completo |
MARC
| LEADER | 00000nam a22000005i 4500 | ||
|---|---|---|---|
| 001 | 978-3-642-30898-7 | ||
| 003 | DE-He213 | ||
| 005 | 20220116124908.0 | ||
| 007 | cr nn 008mamaa | ||
| 008 | 120825s2012 gw | s |||| 0|eng d | ||
| 020 | |a 9783642308987 |9 978-3-642-30898-7 | ||
| 024 | 7 | |a 10.1007/978-3-642-30898-7 |2 doi | |
| 050 | 4 | |a QA299.6-433 | |
| 072 | 7 | |a PBK |2 bicssc | |
| 072 | 7 | |a MAT034000 |2 bisacsh | |
| 072 | 7 | |a PBK |2 thema | |
| 082 | 0 | 4 | |a 515 |2 23 |
| 100 | 1 | |a Annaby, Mahmoud H. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a q-Fractional Calculus and Equations |h [electronic resource] / |c by Mahmoud H. Annaby, Zeinab S. Mansour. |
| 250 | |a 1st ed. 2012. | ||
| 264 | 1 | |a Berlin, Heidelberg : |b Springer Berlin Heidelberg : |b Imprint: Springer, |c 2012. | |
| 300 | |a XIX, 318 p. 6 illus. |b online resource. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a text file |b PDF |2 rda | ||
| 490 | 1 | |a Lecture Notes in Mathematics, |x 1617-9692 ; |v 2056 | |
| 505 | 0 | |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. | |
| 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 | 0 | |a Mathematical analysis. | |
| 650 | 0 | |a Difference equations. | |
| 650 | 0 | |a Functional equations. | |
| 650 | 0 | |a Functions of complex variables. | |
| 650 | 0 | |a Integral equations. | |
| 650 | 0 | |a Mathematical physics. | |
| 650 | 1 | 4 | |a Analysis. |
| 650 | 2 | 4 | |a Difference and Functional Equations. |
| 650 | 2 | 4 | |a Functions of a Complex Variable. |
| 650 | 2 | 4 | |a Integral Transforms and Operational Calculus. |
| 650 | 2 | 4 | |a Integral Equations. |
| 650 | 2 | 4 | |a Mathematical Methods in Physics. |
| 700 | 1 | |a Mansour, Zeinab S. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 710 | 2 | |a SpringerLink (Online service) | |
| 773 | 0 | |t Springer Nature eBook | |
| 776 | 0 | 8 | |i Printed edition: |z 9783642308970 |
| 776 | 0 | 8 | |i Printed edition: |z 9783642308994 |
| 830 | 0 | |a Lecture Notes in Mathematics, |x 1617-9692 ; |v 2056 | |
| 856 | 4 | 0 | |u https://doi.uam.elogim.com/10.1007/978-3-642-30898-7 |z Texto Completo |
| 912 | |a ZDB-2-SMA | ||
| 912 | |a ZDB-2-SXMS | ||
| 912 | |a ZDB-2-LNM | ||
| 950 | |a Mathematics and Statistics (SpringerNature-11649) | ||
| 950 | |a Mathematics and Statistics (R0) (SpringerNature-43713) | ||