Basic theory of fractional differential equations:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New Jersey ; London ; Singapore ; Beijing ; Shanghai ; Hong Kong ; Taipei ; Chennai ; Tokyo
World Scientific
[2017]
|
| Edition: | second edition |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | xii, 367 Seiten |
| ISBN: | 9789813148161 |
Staff View
MARC
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| 100 | 1 | |a Zhou, Yong |d 1964- |e Verfasser |0 (DE-588)1062995449 |4 aut | |
| 245 | 1 | 0 | |a Basic theory of fractional differential equations |c Yong Zhou (Xiangtan University, China), JinRong Wang (Guizhou University, China), Lu Zhang (Xiangtan University, China) |
| 250 | |a second edition | ||
| 264 | 1 | |a New Jersey ; London ; Singapore ; Beijing ; Shanghai ; Hong Kong ; Taipei ; Chennai ; Tokyo |b World Scientific |c [2017] | |
| 300 | |a xii, 367 Seiten | ||
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| 337 | |b n |2 rdamedia | ||
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| 500 | |a Includes bibliographical references and index | ||
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| 650 | 4 | |a Differential equations | |
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Record in the Search Index
| _version_ | 1804176719484026880 |
|---|---|
| adam_text | Contents
Preface to the Second Edition v
Preface to the First Edition vii
1. Preliminaries 1
1.1 Introduction........................................................ 1
1.2 Some Notations, Concepts and Lemmas................................ 1
1.3 Fractional Calculus................................................. 3
1.3.1 Definitions.................................................. 4
1.3.2 Properties .................................................. 9
1.3.3 Mittag-Leffier functions.................................... 12
1.4 Some Results from Nonlinear Analysis............................... 13
1.4.1 Sobolev Spaces.............................................. 13
1.4.2 Measure of Noncompactness................................... 14
1.4.3 Topological Degree.......................................... 15
1.4.4 Picard Operator............................................. 17
1.4.5 Fixed Point Theorems........................................ 18
1.4.6 Critical Point Theorems..................................... 20
1.5 Semigroups......................................................... 22
1.5.1 C{)-semigroup............................................... 22
1.5.2 Almost Sectorial Operators.................................. 23
2. Fractional Functional Differential Equations 27
2.1 Introduction....................................................... 27
2.2 Neutral Equations with Bounded Delay ............................. 28
2.2.1 Introduction................................................ 28
2.2.2 Existence and Uniqueness.................................... 28
2.2.3 Extremal Solutions ......................................... 33
2.3 p-Type Neutral Equations.......................................... 42
2.3.1 Introduction................................................ 42
2.3.2 Existence and Uniqueness.................................... 44
ix
x Basic Theory of Fractional Differential Equations
2.3.3 Continuous Dependence.................................. 55
2.4 Neutral Equations with Infinite Delay ......................... 58
2.4.1 Introduction........................................... 58
2.4.2 Existence and Uniqueness............................... 60
2.4.3 Continuation of Solutions.............................. 67
2.5 Iterative Functional Differential Equations.................... 71
2.5.1 Introduction........................................... 71
2.5.2 Existence ............................................. 72
2.5.3 Data Dependence........................................ 78
2.5.4 Examples and General Cases............................. 79
2.6 Notes and Remarks................................................ 86
3. Fractional Ordinary Differential Equations in Banach Spaces 87
3.1 Introduction..................................................... 87
3.2 Cauchy Problems via Measure of Noncompactness Method .... 89
3.2.1 Introduction............................................. 89
3.2.2 Existence................................................ 89
3.3 Cauchy Problems via Topological Degree Method.................... 98
3.3.1 Introduction............................................. 98
3.3.2 Qualitative Analysis..................................... 98
3.4 Cauchy Problems via Picard Operators Technique...................102
3.4.1 Introduction.............................................102
3.4.2 Results via Picard Operators.............................102
3.4.3 Results via Weakly Picard Operators......................109
3.5 Notes and Remarks................................................113
4. Fractional Abstract Evolution Equations 115
4.1 Introduction.....................................................115
4.2 Evolution Equations with Riemann-Liouville Derivative ...........116
4.2.1 Introduction.............................................116
4.2.2 Definition of Mild Solutions.............................117
4.2.3 Preliminary Lemmas ......................................120
4.2.4 Compact Semigroup Case...................................126
4.2.5 Noncompact Semigroup Case................................131
4.3 Evolution Equations with Caputo Derivative.......................134
4.3.1 Introduction.............................................134
4.3.2 Definition of Mild Solutions.............................134
4.3.3 Preliminary Lemmas ......................................136
4.3.4 Compact Semigroup Case...................................140
4.3.5 Noncompact Semigroup Case................................143
4.4 Nonlocal Problems for Evolution Equations........................145
4.4.1 Introduction.............................................145
Contents xi
4.4.2 Definition of mild solutions...............................145
4.4.3 Existence..................................................147
4.5 Abstract Cauchy Problems with Almost Sectorial Operators .... 153
4.5.1 Introduction...............................................153
4.5.2 Properties of Operators....................................158
4.5.3 Linear Problems............................................164
4.5.4 Nonlinear Problems.........................................169
4.5.5 Applications...............................................177
4.6 Notes and Remarks..................................................179
5. Fractional Impulsive Differential Equations 181
5.1 Introduction.......................................................181
5.2 Impulsive Initial Value Problems...................................182
5.2.1 Introduction...............................................182
5.2.2 Formula of Solutions.......................................182
5.2.3 Existence..................................................185
5.3 Impulsive Boundary Value Problems..................................190
5.3.1 Introduction...............................................190
5.3.2 Formula of Solutions.......................................190
5.3.3 Existence..................................................193
5.4 Impulsive Langevin Equations.......................................197
5.4.1 Introduction...............................................197
5.4.2 Formula of Solutions.......................................198
5.4.3 Existence..................................................206
5.5 Impulsive Evolution Equations .....................................213
5.5.1 Introduction...............................................213
5.5.2 Cauchy Problems ...........................................214
5.5.3 Nonlocal Problems..........................................216
5.6 Notes and Remarks..................................................222
6. Fractional Boundary Value Problems 223
6.1 Introduction.......................................................223
6.2 Solution for В VP with Left and Right Fractional Integrals.........223
6.2.1 Introduction...............................................223
6.2.2 Fractional Derivative Space................................226
6.2.3 Variational Structure......................................231
6.2.4 Existence Under Ambrosetti-Rabinowitz Condition .... 238
6.2.5 Superquadratic Case........................................243
6.2.6 Asymptotically Quadratic Case..............................247
6.3 Multiple Solutions for BVP with Parameters.........................250
6.3.1 Introduction...............................................250
6.3.2 Existence..................................................251
Xll
Basic Theory of Fractional Differential Equations
6.4 Infinite Solutions for В VP with Left and Right Fractional
Integrals..........................................................261
6.4.1 Introduction...............................................261
6.4.2 Existence..................................................262
6.5 Solutions for BVP with Left and Right Fractional Derivatives . . . 271
6.5.1 Introduction...............................................271
6.5.2 Variational Structure......................................272
6.5.3 Existence of Weak Solutions................................275
6.5.4 Existence of Solutions.....................................279
6.6 Notes and Remarks..................................................283
7. Fractional Partial Differential Equations 285
7.1 Introduction.......................................................285
7.2 Fractional Navier-Stokes Equations.................................285
7.2.1 Introduction...............................................285
7.2.2 Preliminaries..............................................287
7.2.3 Global Existence...........................................290
7.2.4 Local Existence ...........................................297
7.2.5 Regularity.................................................301
7.3 Fractional Euler-Lagrange Equations................................309
7.3.1 Introduction...............................................309
7.3.2 Functional Spaces..........................................311
7.3.3 Variational Structure......................................314
7.3.4 Existence of Weak Solution.................................317
7.4 Fractional Diffusion Equations.....................................321
7.4.1 Introduction...............................................321
7.4.2 Preliminaries..............................................324
7.4.3 Existence and Regularity...................................327
7.5 Fractional Schrodinger Equations...................................336
7.5.1 Introduction...............................................336
7.5.2 Preliminaries..............................................337
7.5.3 Existence and Uniqueness...................................340
7.6 Notes and Remarks..................................................342
Bibliography 343
Index 363
|
| any_adam_object | 1 |
| author | Zhou, Yong 1964- Wang, JinRong Zhang, Lu |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.352 |
| dewey-search | 515/.352 |
| dewey-sort | 3515 3352 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | second edition |
| format | Book |
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| id | DE-604.BV043848279 |
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| language | English |
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| spelling | Zhou, Yong 1964- Verfasser (DE-588)1062995449 aut Basic theory of fractional differential equations Yong Zhou (Xiangtan University, China), JinRong Wang (Guizhou University, China), Lu Zhang (Xiangtan University, China) second edition New Jersey ; London ; Singapore ; Beijing ; Shanghai ; Hong Kong ; Taipei ; Chennai ; Tokyo World Scientific [2017] xii, 367 Seiten txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Fractional differential equations Differential equations Fractional calculus Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Gebrochene Analysis (DE-588)4722475-7 gnd rswk-swf Ableitung gebrochener Ordnung (DE-588)4365956-1 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 s Ableitung gebrochener Ordnung (DE-588)4365956-1 s DE-604 Gebrochene Analysis (DE-588)4722475-7 s 1\p DE-604 Wang, JinRong Verfasser aut Zhang, Lu Verfasser aut Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029258664&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Zhou, Yong 1964- Wang, JinRong Zhang, Lu Basic theory of fractional differential equations Fractional differential equations Differential equations Fractional calculus Differentialgleichung (DE-588)4012249-9 gnd Gebrochene Analysis (DE-588)4722475-7 gnd Ableitung gebrochener Ordnung (DE-588)4365956-1 gnd |
| subject_GND | (DE-588)4012249-9 (DE-588)4722475-7 (DE-588)4365956-1 |
| title | Basic theory of fractional differential equations |
| title_auth | Basic theory of fractional differential equations |
| title_exact_search | Basic theory of fractional differential equations |
| title_full | Basic theory of fractional differential equations Yong Zhou (Xiangtan University, China), JinRong Wang (Guizhou University, China), Lu Zhang (Xiangtan University, China) |
| title_fullStr | Basic theory of fractional differential equations Yong Zhou (Xiangtan University, China), JinRong Wang (Guizhou University, China), Lu Zhang (Xiangtan University, China) |
| title_full_unstemmed | Basic theory of fractional differential equations Yong Zhou (Xiangtan University, China), JinRong Wang (Guizhou University, China), Lu Zhang (Xiangtan University, China) |
| title_short | Basic theory of fractional differential equations |
| title_sort | basic theory of fractional differential equations |
| topic | Fractional differential equations Differential equations Fractional calculus Differentialgleichung (DE-588)4012249-9 gnd Gebrochene Analysis (DE-588)4722475-7 gnd Ableitung gebrochener Ordnung (DE-588)4365956-1 gnd |
| topic_facet | Fractional differential equations Differential equations Fractional calculus Differentialgleichung Gebrochene Analysis Ableitung gebrochener Ordnung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029258664&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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