Basic theory of fractional differential equations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New Jersey ; Singapore
World Scientific
[2014]
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverzeichnis Seite 279-293 |
| Physical Description: | x, 293 Seiten |
| ISBN: | 9789814579896 |
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Record in the Search Index
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| adam_text | Titel: Basic theory of fractional differential equations
Autor: Zhou, Yong
Jahr: 2014
Contents
Preface v
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......................................................8
1.4 Some Results from Nonlinear Analysis................................11
1.4.1 Sobolev Spaces..................................................11
1.4.2 Measure of Noncompactness..................................12
1.4.3 Topological Degree ............................................13
1.4.4 Picard Operator................................................15
1.4.5 Fixed Point Theorems..........................................16
1.4.6 Critical Point Theorems ......................................17
1.5 Semigroups..............................................................20
1.5.1 Co-Semigroup..................................................20
1.5.2 Almost Sectorial Operators....................................21
2. Fractional Functional Differential Equations 23
2.1 Introduction..............................................................23
2.2 Neutral Equations with Bounded Delay..............................24
2.2.1 Introduction....................................................24
2.2.2 Existence and Uniqueness......................................24
2.2.3 Extremal Solutions............................................29
2.3 p-Type Neutral Equations..............................................38
2.3.1 Introduction...............................38
2.3.2 Existence and Uniqueness......................................40
2.3.3 Continuous Dependence........................................50
2.4 Neutral Equations with Infinite Delay................................53
2.4.1 Introduction....................................................53
2.4.2 Existence and Uniqueness......................................55
2.4.3 Continuation of Solutions......................................62
2.5 Iterative Functional Differential Equations............................66
2.5.1 Introduction..............................66
2.5.2 Existence ......................................................66
2.5.3 Data Dependence..............................................72
2.5.4 Examples and General Cases..................................74
2.6 Notes and Remarks......................................................80
3. Fractional Ordinary Differential Equations in Banach Spaces 81
3.1 Introduction............................... 81
3.2 Cauchy Problems via Measure of Noncompactness Method .... 83
3.2.1 Introduction.......................... 83
3.2.2 Existence............................ 83
3.3 Cauchy Problems via Topological Degree Method.......... 92
3.3.1 Introduction.......................... 92
3.3.2 Qualitative Analysis...................... 92
3.4 Cauchy Problems via Picard Operators Technique ......... 96
3.4.1 Introduction....................................................96
3.4.2 Results via Picard Operators..................................96
3.4.3 Results via Weakly Picard Operators............102
3.5 Notes and Remarks...........................107
4. Fractional Abstract Evolution Equations 109
4.1 Introduction...............................109
4.2 Evolution Equations with Riemann-Liouville Derivative......110
4.2.1 Introduction..........................110
4.2.2 Definition of Mild Solutions .................Ill
4.2.3 Preliminary Lemmas.....................114
4.2.4 Compact Semigroup Case...................120
4.2.5 Noncompact Semigroup Case.................124
4.3 Evolution Equations with Caputo Derivative ............127
4.3.1 Introduction..........................127
4.3.2 Definition of Mild Solutions .................128
4.3.3 Preliminary Lemmas.....................130
4.3.4 Compact Semigroup Case...................133
4.3.5 Noncompact Semigroup Case.................136
4.4 Nonlocal Cauchy Problems for Evolution Equations ........138
4.4.1 Introduction..........................138
4.4.2 Definition of Mild Solutions .................139
4.4.3 Existence............................140
4.5 Abstract Cauchy Problems with Almost Sectorial Operators .... 146
4.5.1 Introduction..........................146
4.5.2 Preliminaries..........................150
4.5.3 Properties of Operators....................154
4.5.4 Linear Problems........................160
4.5.5 Nonlinear Problems......................164
4.5.6 Applications..........................172
4.6 Notes and Remarks...........................175
Fractional Boundary Value Problems via Critical Point Theory 177
5.1 Introduction...............................177
5.2 Existence of Solution for EVP with Left and Right Fractional
Integrals.................................177
5.2.1 Introduction..........................177
5.2.2 Fractional Derivative Space..................180
5.2.3 Variational Structure.....................185
5.2.4 Existence under Ambrosetti-Rabinowitz Condition.....192
5.2.5 Superquadratic Case .....................196
5.2.6 Asymptotically Quadratic Case ...............200
5.3 Multiple Solutions for BVP with Parameters ............203
5.3.1 Introduction..........................203
5.3.2 Existence............................204
5.4 Infinite Solutions for BVP with Left and Right Fractional Integrals 214
5.4.1 Introduction..........................214
5.4.2 Existence............................215
5.5 Existence of Solutions for BVP with Left and Right Fractional
Derivatives ...............................223
5.5.1 Introduction..........................223
5.5.2 Variational Structure.....................224
5.5.3 Existence of Weak Solutions.................227
5.5.4 Existence of Solutions.....................231
5.6 Notes and Remarks...........................235
Fractional Partial Differential Equations 237
6.1 Introduction...............................237
6.2 Fractional Euler-Lagrange Equations.................237
6.2.1 Introduction..........................237
6.2.2 Functional Spaces.......................239
6.2.3 Variational Structure.....................242
6.2.4 Existence of Weak Solution..................245
6.3 Time-Fractional Diffusion Equations.................249
6.3.1 Introduction..........................249
6.3.2 Regularity and Unique Existence...............250
6.4 Fractional Hamiltonian Systems....................257
6.4.1 Introduction..........................257
6.4.2 Fractional Derivative Space..................257
6.4.3 Existence and Multiplicity..................263
6.5 Fractional Schrödinger Equations...................271
6.5.1 Introduction..........................271
6.5.2 Existence and Uniqueness...................273
6.6 Notes and Remarks...........................278
Bibliography 279
|
| any_adam_object | 1 |
| author | Zhou, Yong 1964- |
| author_GND | (DE-588)1062995449 |
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| dewey-sort | 3515.35 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV042034331 |
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| language | English |
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| physical | x, 293 Seiten |
| publishDate | 2014 |
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| publisher | World Scientific |
| record_format | marc |
| spelling | Zhou, Yong 1964- Verfasser (DE-588)1062995449 aut Basic theory of fractional differential equations Yong Zhou, Xiangtan University, China New Jersey ; Singapore World Scientific [2014] © 2014 x, 293 Seiten txt rdacontent n rdamedia nc rdacarrier Literaturverzeichnis Seite 279-293 Gebrochene Analysis (DE-588)4722475-7 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Ableitung gebrochener Ordnung (DE-588)4365956-1 gnd rswk-swf Gebrochene Analysis (DE-588)4722475-7 s DE-604 Differentialgleichung (DE-588)4012249-9 s Ableitung gebrochener Ordnung (DE-588)4365956-1 s 1\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027475743&sequence=000002&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- Basic theory of fractional differential equations Gebrochene Analysis (DE-588)4722475-7 gnd Differentialgleichung (DE-588)4012249-9 gnd Ableitung gebrochener Ordnung (DE-588)4365956-1 gnd |
| subject_GND | (DE-588)4722475-7 (DE-588)4012249-9 (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 |
| title_fullStr | Basic theory of fractional differential equations Yong Zhou, Xiangtan University, China |
| title_full_unstemmed | Basic theory of fractional differential equations Yong Zhou, Xiangtan University, China |
| title_short | Basic theory of fractional differential equations |
| title_sort | basic theory of fractional differential equations |
| topic | Gebrochene Analysis (DE-588)4722475-7 gnd Differentialgleichung (DE-588)4012249-9 gnd Ableitung gebrochener Ordnung (DE-588)4365956-1 gnd |
| topic_facet | Gebrochene Analysis Differentialgleichung Ableitung gebrochener Ordnung |
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