Asymptotic integration and stability: for ordinary, functional and discrete differential equations of fractional order
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Singapore [u.a.]
World Scientific
2015
|
| Series: | Series on complexity, nonlinearity and chaos
4 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XI, 196 S. |
| ISBN: | 9789814641098 |
Staff View
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| 245 | 1 | 0 | |a Asymptotic integration and stability |b for ordinary, functional and discrete differential equations of fractional order |c Dumitru Baleanu ; Octavian G. Mustafa |
| 264 | 1 | |a Singapore [u.a.] |b World Scientific |c 2015 | |
| 300 | |a XI, 196 S. | ||
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| 650 | 4 | |a Fractional differential equations | |
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Record in the Search Index
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| adam_text | Titel: Asymptotic integration and stability
Autor: Baleanu, Dumitru
Jahr: 2015
Contents
Preface vii
1. The Differential Operators of Order 1 + o and Their
Integral Counterparts 1
1.1 The Gamma Function 2
1.2 The Riemann-Liouville Derivative 3
1.3 The Abel Computation 19
1.4 The Operators. The Caputo Differential 21
1.5 The Integral Representation of the Operators.
The Half-line Case 23
2. Existence and Uniqueness of Solution for the Differential
Equations of Order a 27
2.1 A Lovelady-Martin Uniqueness Result for the
Equation (2.2) 34
2.2 A Nagumo-like Uniqueness Criterion
for the Fractional Differential Equations
with a Riemann-Liouville Derivative 39
2.3 A Wintner-type Existence Interval for the
Equation (2.2) 45
3. Position of the Zeros, the Bihari Inequality, and the
Asymptotic Behavior of Solutions for the Differential
Equations of Order a 51
3.1 A Fite-type Length Criterion for Fractional
Disconjugacy 51
ix
x Asymptotic Integration and Stability
3.2 The Bihari Inequality 55
3.3 Asymptotic Integration of the Differential Equations
of Orders 1 and a 61
3.4 The Bihari Asymptotic Integration
Theory of the Differential Equations of Second Order ... 76
4. Asymptotic Integration for the Differential Equations of
Order 1 + a 79
4.1 An Asymptotic Integration Theory of Trench Type .... 79
4.2 Asymptotically Linear Solutions 90
4.3 A Bihari-Like Result 95
4.4 Convergent Solutions 104
4.5 Lp-Solutions of the Equation (4.3) 109
5. Existence and Uniqueness of Solution for Some Delay
Differential Equations with Caputo Derivatives 121
6. Existence of Positive Solutions for Some Delay Fractional
Differential Equations with a Generalized N Teriri 129
6.1 The Existence Theorem 130
6.2 Existence and Uniqueness for the Solution 137
7. Stability of a Class of Discrete Fractional
Nonautonomous Systems 139
7.0.1 Preliminaries 139
7.0.2 The Lyapunov Method for Discrete Fractional
Nonautonomous Systems 140
8. Mittag-LefRer Stability of Fractional Nonlinear Systems
with Delay 145
9. Razumikhin Stability for Fractional Systems in the
Presence of Delay 151
10. Controllability of Some Fractional Evolution Nonlocal
Impulsive Quasilinear Delay Integro-Differential Systems 157
Contents xi
10.1 Preliminaries 157
10.2 The Problem 161
10.3 A Controllability Result 162
11. Approximate Controllability of Sobolev Type Nonlocal
Fractional Stochastic Dynamic Systems in Hilbert Spaces 169
11.0.1 The Problem 170
11.0.2 Approximate Controllability 175
Bibliography 181
Index 195
|
| any_adam_object | 1 |
| author | Baleanu, Dumitru 1964- Mustafa, Octavian G. |
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| id | DE-604.BV042403480 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:20:36Z |
| institution | BVB |
| isbn | 9789814641098 |
| language | English |
| lccn | 014045570 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027839121 |
| oclc_num | 911190280 |
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| owner | DE-703 DE-19 DE-BY-UBM DE-634 DE-20 DE-11 |
| owner_facet | DE-703 DE-19 DE-BY-UBM DE-634 DE-20 DE-11 |
| physical | XI, 196 S. |
| publishDate | 2015 |
| publishDateSearch | 2015 |
| publishDateSort | 2015 |
| publisher | World Scientific |
| record_format | marc |
| series | Series on complexity, nonlinearity and chaos |
| series2 | Series on complexity, nonlinearity and chaos |
| spelling | Baleanu, Dumitru 1964- Verfasser (DE-588)1025757629 aut Asymptotic integration and stability for ordinary, functional and discrete differential equations of fractional order Dumitru Baleanu ; Octavian G. Mustafa Singapore [u.a.] World Scientific 2015 XI, 196 S. txt rdacontent n rdamedia nc rdacarrier Series on complexity, nonlinearity and chaos 4 Includes bibliographical references and index Fractional calculus Fractional differential equations Asymptotische Integration (DE-588)4299140-7 gnd rswk-swf Asymptotische Integration (DE-588)4299140-7 s DE-604 Mustafa, Octavian G. Verfasser (DE-588)1072494892 aut Series on complexity, nonlinearity and chaos 4 (DE-604)BV040459766 4 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027839121&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Baleanu, Dumitru 1964- Mustafa, Octavian G. Asymptotic integration and stability for ordinary, functional and discrete differential equations of fractional order Series on complexity, nonlinearity and chaos Fractional calculus Fractional differential equations Asymptotische Integration (DE-588)4299140-7 gnd |
| subject_GND | (DE-588)4299140-7 |
| title | Asymptotic integration and stability for ordinary, functional and discrete differential equations of fractional order |
| title_auth | Asymptotic integration and stability for ordinary, functional and discrete differential equations of fractional order |
| title_exact_search | Asymptotic integration and stability for ordinary, functional and discrete differential equations of fractional order |
| title_full | Asymptotic integration and stability for ordinary, functional and discrete differential equations of fractional order Dumitru Baleanu ; Octavian G. Mustafa |
| title_fullStr | Asymptotic integration and stability for ordinary, functional and discrete differential equations of fractional order Dumitru Baleanu ; Octavian G. Mustafa |
| title_full_unstemmed | Asymptotic integration and stability for ordinary, functional and discrete differential equations of fractional order Dumitru Baleanu ; Octavian G. Mustafa |
| title_short | Asymptotic integration and stability |
| title_sort | asymptotic integration and stability for ordinary functional and discrete differential equations of fractional order |
| title_sub | for ordinary, functional and discrete differential equations of fractional order |
| topic | Fractional calculus Fractional differential equations Asymptotische Integration (DE-588)4299140-7 gnd |
| topic_facet | Fractional calculus Fractional differential equations Asymptotische Integration |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027839121&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV040459766 |
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