Fractional differentiation inequalities:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer
2009
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 675 S. |
| ISBN: | 9780387981277 |
Internformat
MARC
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| 100 | 1 | |a Anastassiou, George A. |d 1952- |e Verfasser |0 (DE-588)121815900 |4 aut | |
| 245 | 1 | 0 | |a Fractional differentiation inequalities |c George A. Anastassiou |
| 264 | 1 | |a New York, NY |b Springer |c 2009 | |
| 300 | |a XIV, 675 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Differential inequalities | |
| 650 | 4 | |a Fractional calculus | |
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Datensatz im Suchindex
| _version_ | 1804139315298566144 |
|---|---|
| adam_text | Contents
Preface
xiii
1
Introduction
1
2
Opial-Type
Inequalities for Functions and Their Ordinary
and Canavati Fractional Derivatives
7
2.1
Preliminaries
.......................... 7
2.2
Main Results
.......................... 11
2.3
Applications
........................... 18
3
Canavati Fractional Opial-Type Inequalities and Fractional
Differential Equations
23
3.1
Introduction
........................... 23
3.2
Preliminaries
.......................... 24
3.3
Main Results
.......................... 26
3.4
Applications
........................... 34
3.5
Other Fractional Differential Equations
........... 38
4
Riemann—Liouville Opial-Type Inequalities for Fractional
Derivatives
41
4.1
Introduction and Preliminaries
................ 41
4.2
Main Results
.......................... 44
4.3
Applications
........................... 48
viii Contents
5
Opial
-Туре
.^-Inequalities for Riemann-Liouville
Fractional Derivatives
53
5.1
Introduction and Preliminaries
................ 53
5.2
Main Results
.......................... 56
6
Opial
-Туре
Inequalities Involving Canavati Fractional
Derivatives of Two Functions and Applications
67
6.1
Introduction
........................... 67
6.2
Preliminaries
.......................... 69
6.3
Main Results
.......................... 72
6.4
Applications
........................... 96
7
Opial
-Туре
Inequalities for Riemann-Liouville Fractional
Derivatives of Two Functions with Applications
107
7.1
Introduction
........................... 107
7.2
Background
........................... 108
7.3
Main Results
.......................... 109
7.4
Applications
........................... 138
8
Canavati Fractional
Opial
-Туре
Inequalities for Several
Functions and Applications
149
8.1
Introduction
........................... 149
8.2
Preliminaries
.......................... 150
8.3
Main Results
.......................... 152
8.4
Applications
........................... 169
9
Riemann—Liouville Fractional
Opial
-Туре
Inequalities
for Several Functions and Applications
179
9.1
Introduction
........................... 179
9.2
Background
........................... 180
9.3
Main Results
.......................... 181
9.4
Applications
........................... 195
10
Converse Canavati Fractional
Opial
-Туре
Inequalities
for Several Functions
205
10.1
Introduction
........................... 205
10.2
Preliminaries
.......................... 206
10.3
Main Results
.......................... 209
10.3.1
Results Involving Two Functions
........... 209
10.3.2
Results Involving Several Functions
......... 220
11
Converse Riemann-Liouville Fractional Opial-Type
Inequalities for Several Functions
229
11.1
Introduction
........................... 229
11.2
Background
........................... 230
Contents ix
11.3 Main
Results..........................
231
11.3.1
Results Involving Two Functions
........... 231
11.3.2
Results Involving Several Functions
......... 244
11.3.3
Results with Respect to Generalized Riemann
-
Liouville Fractional Derivative
............ 251
12
Multivariate Canavati Fractional Taylor Formula
257
12.1
Introduction
........................... 257
12.2
Results
.............................. 258
13
Multivariate
Caputo
Fractional Taylor Formula
269
13.1
Background
........................... 269
13.2
Results
.............................. 270
14
Canavati Fractional Multivariate Opial-Type
Inequalities on Spherical Shells
279
14.1
Introduction
........................... 279
14.2
Results
.............................. 280
15
Riemann—Liouville Fractional Multivariate Opial-Type
Inequalities over a Spherical Shell
319
15.1
Introduction
........................... 319
15.2
Background—I
......................... 320
15.3
Background—II
......................... 323
15.4
Background—III
........................ 329
15.5
Main Results
.......................... 334
15.5.1
Riemann-Liouville Fractional Opial-Type
Inequalities Involving One Function
......... 334
15.5.2
Riemann-Liouville Fractional Opial-Type
Inequalities Involving Two Functions
......... 350
15.5.3
Riemann-Liouville Fractional Opial-Type
Inequalities Involving Several Functions
....... 369
16
Caputo
Fractional Multivariate Opial-Type Inequalities
over a Spherical Shell
391
16.1
Introduction
........................... 391
16.2
Background—I
......................... 392
16.3
Main Results
.......................... 397
16.3.1
Results Involving One Function
............ 397
16.3.2
Results Involving Two Functions
........... 402
16.3.3
Results Involving Several Functions
......... 411
16.4
Background—II
......................... 419
16.5
Main Results on a Spherical Shell
............... 424
16.5.1
Results Involving One Function
............ 424
16.5.2
Results Involving Two Functions
........... 427
χ
Contents
16.5.3
Results Involving Several Functions
.........431
16.6
Applications
...........................436
17
Poincaré-Type
Fractional Inequalities
445
17.1
Introduction
........................... 445
17.2
Fractional
Poincaré
Inequalities Results
........... 446
17.3
Applications of Fractional
Poincaré
Inequalities
....... 457
17.4
Fractional Mean
Poincaré
Inequalities
............ 473
17.5
Applications of Fractional Mean
Poincaré
Inequalities
. . . 479
18
Various Sobolev-Type Fractional Inequalities
483
18.1
Introduction
........................... 483
18.2
Various Univariate Sobolev-Type Fractional Inequalities
. . 484
18.3
Applications
........................... 503
19
General Hubert—Pachpatte-Type Integral Inequalities
505
19.1
Introduction
...........................505
19.2
Main Results
..........................506
20
General Multivariate Hubert—Pachpatte-Type
Integral Inequalities
523
20.1
Introduction
........................... 523
20.2
Symbols and Basics
....................... 524
20.3
Main Results
.......................... 527
21
Other Hubert—Pachpatte-Type Fractional Integral
Inequalities
545
21.1
Background
........................... 545
21.2
Univariate Results
....................... 550
21.3
Multivariate Results
...................... 553
22
Canavati Fractional and Other Approximation
of Csiszar s /-Divergence
563
22.1
Preliminaries
..........................563
22.2
Main Results
..........................568
23
Caputo
and Riemann—Liouville Fractional
Approximation of Csiszar s /-Divergence
577
23.1
Preliminaries
.......................... 577
23.2
Results
.............................. 581
24
Canavati Fractional
Ostrowski
-Туре
Inequalities
589
24.1
Background
...........................589
24.2
Results
..............................591
Contents xi
25 Multivariate Canavati
Fractional
Ostrowski-Type
Inequalities
595
25.1
Background...........................
595
25.2
Results
.............................. 598
26
Caputo
Fractional
Ostrowski-Type
Inequalities
615
26.1
Background
........................... 615
26.2
Univariate Results
....................... 618
26.3
Multivariate Results
...................... 622
27
Appendix
635
27.1
Conversion Formulae for Different Kinds of Fractional
Derivatives
........................... 635
27.2
Some Basic Fractional Derivatives
.............. 638
References
641
List of Symbols
671
Index
673
|
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| id | DE-604.BV035636606 |
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| indexdate | 2024-07-09T21:42:08Z |
| institution | BVB |
| isbn | 9780387981277 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017691455 |
| oclc_num | 426116706 |
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| physical | XIV, 675 S. |
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| spelling | Anastassiou, George A. 1952- Verfasser (DE-588)121815900 aut Fractional differentiation inequalities George A. Anastassiou New York, NY Springer 2009 XIV, 675 S. txt rdacontent n rdamedia nc rdacarrier Differential inequalities Fractional calculus Ableitung gebrochener Ordnung (DE-588)4365956-1 gnd rswk-swf Differentialungleichung (DE-588)4149785-5 gnd rswk-swf Ableitung gebrochener Ordnung (DE-588)4365956-1 s Differentialungleichung (DE-588)4149785-5 s DE-604 Erscheint auch als Online-Ausgabe 978-0-387-98128-4 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017691455&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Anastassiou, George A. 1952- Fractional differentiation inequalities Differential inequalities Fractional calculus Ableitung gebrochener Ordnung (DE-588)4365956-1 gnd Differentialungleichung (DE-588)4149785-5 gnd |
| subject_GND | (DE-588)4365956-1 (DE-588)4149785-5 |
| title | Fractional differentiation inequalities |
| title_auth | Fractional differentiation inequalities |
| title_exact_search | Fractional differentiation inequalities |
| title_full | Fractional differentiation inequalities George A. Anastassiou |
| title_fullStr | Fractional differentiation inequalities George A. Anastassiou |
| title_full_unstemmed | Fractional differentiation inequalities George A. Anastassiou |
| title_short | Fractional differentiation inequalities |
| title_sort | fractional differentiation inequalities |
| topic | Differential inequalities Fractional calculus Ableitung gebrochener Ordnung (DE-588)4365956-1 gnd Differentialungleichung (DE-588)4149785-5 gnd |
| topic_facet | Differential inequalities Fractional calculus Ableitung gebrochener Ordnung Differentialungleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017691455&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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