Implicit fractional differential and integral equations: existence and stability
Gespeichert in:
| Hauptverfasser: | , , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin
De Gruyter
[2018]
|
| Schriftenreihe: | De Gruyter series in nonlinear analysis and applications
Volume 26 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110553130&searchTitles=true Inhaltsverzeichnis |
| Beschreibung: | XXIII, 336 Seiten 24 cm |
| ISBN: | 9783110553130 3110553139 |
Internformat
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| 245 | 1 | 0 | |a Implicit fractional differential and integral equations |b existence and stability |c Saïd Abbas, Mouffak Benchohra, John R. Graef, Johnny Henderson |
| 264 | 1 | |a Berlin |b De Gruyter |c [2018] | |
| 300 | |a XXIII, 336 Seiten |c 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
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| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a De Gruyter series in nonlinear analysis and applications |v Volume 26 | |
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| 650 | 0 | 7 | |a Funktional-Differentialgleichung |0 (DE-588)4155668-9 |2 gnd |9 rswk-swf |
| 653 | |a Differentialgleichung | ||
| 653 | |a Existenzsatz | ||
| 653 | |a Gebrochene Analysis | ||
| 653 | |a Integralgleichung | ||
| 653 | |a Stabilität | ||
| 689 | 0 | 0 | |a Funktional-Differentialgleichung |0 (DE-588)4155668-9 |D s |
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| 700 | 1 | |a Benchohra, Mouffak |e Verfasser |0 (DE-588)136868207 |4 aut | |
| 700 | 1 | |a Graef, John R. |d 1942- |e Verfasser |0 (DE-588)140965459 |4 aut | |
| 700 | 1 | |a Henderson, Johnny |e Verfasser |0 (DE-588)170788350 |4 aut | |
| 710 | 2 | |a Walter de Gruyter GmbH & Co. KG |0 (DE-588)10095502-2 |4 pbl | |
| 776 | 0 | 8 | |i Elektronische Reproduktion |z 9783110553185 |
| 776 | 0 | 8 | |i Elektronische Reproduktion |z 9783110553819 |
| 776 | 0 | 8 | |i Erscheint auch als |z 9783110553826 |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |a Abbas, Saïd |t Implicit Fractional Differential and Integral Equations |d Berlin/Boston : De Gruyter, 2018 |h Online-Ressourcen, 359 Seiten |
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Datensatz im Suchindex
| _version_ | 1804179078442385408 |
|---|---|
| adam_text | CONTENTS
PREFACE* VII
INTRODUCTION * XV
1 PRELIMINARY BACKGROUND * 1
1.1 NOTATIONS AND DEFINITIONS * 1
1.2 FRACTIONAL CALCULUS
----
2
1.3 MULTIVALUED ANALYSIS * 5
1.4 MEASURE OF NONCOMPACTNESS * 7
1.5 PHASE SPACES * 9
1.5.1 EXAMPLES OF PHASE SPACES * 9
1.6 SOME FIXED POINT THEOREMS *
10
1.7 AUXILIARY LEMMAS
----
12
2 NONLINEAR IMPLICIT FRACTIONAL DIFFERENTIAL EQUATIONS * 15
2.1 INTRODUCTION
-----
15
2.2 EXISTENCE AND STABILITY RESULTS FOR NIFDE
----
15
2.2.1 INTRODUCTION AND MOTIVATIONS * 15
2.2.2 EXISTENCE OF SOLUTIONS
------
16
2.2.3 EXAMPLES
----
22
2.3 NIFDE WITH NONLOCAL CONDITIONS
----
23
2.3.1 INTRODUCTION AND MOTIVATIONS * 23
2.3.2 EXISTENCE OF SOLUTIONS
------
23
2.3.3 STABILITY RESULTS * 29
2.3.4 AN EXAMPLE
----
30
2.4 EXISTENCE RESULTS FOR NIFDE IN BANACH SPACE * 31
2.4.1 INTRODUCTION AND MOTIVATIONS * 31
2.4.2 EXISTENCE OF SOLUTIONS
------
32
2.4.3 AN EXAMPLE
----
37
2.5 EXISTENCE AND STABILITY RESULTS FOR PERTURBED NIFDE WITH FINITE
DELAY
----
37
2.5.1 INTRODUCTION
-----
37
2.5.2 EXISTENCE OF SOLUTIONS
------
38
2.5.3 ULAM-HYERS STABILITY RESULTS * 43
2.5.4 AN EXAMPLE
----
47
2.6 EXISTENCE AND STABILITY RESULTS FOR NEUTRAL NIFDE WITH FINITE DELAY
2.6.1 INTRODUCTION
-----
47
2.6.2 EXISTENCE OF SOLUTIONS
------
48
2.6.3 ULAM-HYERS STABILITY RESULTS
----
50
2.6.4
2.7
3
3.1
3.2
3
.
2.1
3.2.2
3.2.3
3.2.4
3.3
3.3.1
3.3.2
3.3.3
3.4
3.4.1
3.4.2
3.4.3
3.4.4
3.5
3.5.1
3.5.2
3.5.3
3.5.4
3.6
4
4.1
4.2
4.2.1
4.2.2
4.2.3
4.3
4.3.1
4.3.2
4.3.3
4.4
EXAMPLES
----
53
NOTES AND REMARKS
----
55
IMPULSIVE NONLINEAR IMPLICIT FRACTIONAL DIFFERENTIAL EQUATIONS * 56
INTRODUCTION
----
56
EXISTENCE AND STABILITY RESULTS FOR IMPULSIVE NLFDES WITH FINITE
DELAY
----
56
INTRODUCTION
----
56
EXISTENCE OF SOLUTIONS
----
57
ULAM-HYERS-RASSIAS STABILITY
----
66
EXAMPLES
----
71
EXISTENCE RESULTS FOR IMPULSIVE NIFDE WITH FINITE DELAY IN BANACH
SPACE
----
73
INTRODUCTION
----
73
EXISTENCE OF SOLUTIONS
----
73
EXAMPLES
----
81
EXISTENCE AND STABILITY RESULTS FOR PERTURBED IMPULSIVE NIFDE WITH
FINITE
DELAY
----
83
INTRODUCTION
----
83
EXISTENCE OF SOLUTIONS
----
83
ULAM-HYERS STABILITY RESULTS
----
93
EXAMPLES
----
98
EXISTENCE AND STABILITY RESULTS FOR NEUTRAL IMPULSIVE NIFDE WITH FINITE
DELAY
----
100
INTRODUCTION
----
100
EXISTENCE OF SOLUTIONS
----
100
ULAM-HYERS STABILITY RESULTS
----
110
AN EXAMPLE
----
115
NOTES AND REMARKS * 116
BOUNDARY VALUE PROBLEMS FOR NONLINEAR IMPLICIT FRACTIONAL DIFFERENTIAL
EQUATIONS * 117
INTRODUCTION
----
117
BVP FOR NIFDE WITH 0
A
1
----
117
INTRODUCTION AND MOTIVATIONS
----
117
EXISTENCE OF SOLUTIONS
----
117
EXAMPLES
----
124
BVP FOR NIFDE WITH 1
A
2
----
125
INTRODUCTION AND MOTIVATIONS
----
125
EXISTENCE OF SOLUTIONS
----
126
EXAMPLES
----
133
STABILITY RESULTS FOR BVP FOR NIFDE
----
134
4.4.1 INTRODUCTION AND MOTIVATIONS
-----
134
4.4.2 EXISTENCE OF SOLUTIONS
----
134
4.4.3 ULAM-HYERS-RASSIAS STABILITY
-----
139
4.4.4 EXAMPLES
-----
144
4.5 BVP FOR NIFDE IN BANACH SPACE
----
145
4.5.1 INTRODUCTION AND MOTIVATIONS
-----
145
4.5.2 EXISTENCE RESULTS FOR BVPS IN BANACH SPACE
----
146
4.5.3 EXISTENCE RESULTS FOR NONLOCAL BVP IN BANACH SPACE
----
152
4.5.4 EXAMPLES
-----
153
4.6 I?-SOLUTIONS OF BVP FOR NIFDE
-----
155
4.6.1 INTRODUCTION AND MOTIVATIONS
-----
155
4.6.2 EXISTENCE OF SOLUTIONS
----
156
4.6.3 NONLOCAL PROBLEM
----
160
4.6.4 EXAMPLES
-----
162
4.7 NOTES AND REMARKS
-----
163
5 BOUNDARY VALUE PROBLEMS FOR IMPULSIVE NIFDE * 164
5.1 INTRODUCTION AND MOTIVATIONS
-----
164
5.2 EXISTENCE RESULTS FOR IMPULSIVE NLFDES
----
164
5.2.1 INTRODUCTION
-----
164
5.2.2 EXISTENCE OF SOLUTIONS
-----
164
5.2.3 ULAM-HYERS RASSIAS STABILITY
----
174
5.2.4 EXAMPLES
-----
179
5.3 EXISTENCE RESULTS FOR IMPULSIVE NIFDE IN BANACH SPACE
-----
181
5.3.1 INTRODUCTION
-----
181
5.3.2 EXISTENCE OF SOLUTIONS
----
181
5.3.3 EXAMPLES
-----
189
5.4 NOTES AND REMARKS
-----
191
6 INTEGRABLE SOLUTIONS FOR IMPLICIT FRACTIONAL DIFFERENTIAL EQUATIONS *
192
6.1 INTRODUCTION
-----
192
6.2 INTEGRABLE SOLUTIONS FOR NIFDE
----
192
6.2.1 INTRODUCTION
-----
192
6.2.2 EXISTENCE OF SOLUTIONS
-----
192
6.2.3 EXAMPLE
----
196
6.3 -SOLUTIONS FOR NLFDES WITH NONLOCAL CONDITIONS
----
197
6.3.1 INTRODUCTION
-----
197
6.3.2 EXISTENCE OF SOLUTIONS
-----
197
6.3.3 EXAMPLE
----
202
6.4 INTEGRABLE SOLUTIONS FOR NLFDES WITH INFINITE DELAY
----
203
6.4.1 INTRODUCTION
-----
203
6.4.2 EXISTENCE OF SOLUTIONS
-----
203
6.4.3
6.5
6.5.1
6.5.2
6.5.3
6.6
7
7.1
7.2
7.2.1
7.2.2
7.2.3
7.3
7.3.1
7.3.2
7.3.3
7.4
7.4.1
7.4.2
7.4.3
7.5
8
8.1
8.2
8
.
2.1
8
.
2.2
8.2.3
8.3
8.3.1
8.3.2
8.3.3
8.4
8.4.1
EXAMPLE
----
207
AN EXISTENCE RESULT OF INTEGRABLE SOLUTIONS FOR NLFDES
----
209
INTRODUCTION
----
209
EXISTENCE OF SOLUTIONS
----
209
EXAMPLE
----
213
NOTES AND REMARKS
----
214
PARTIAL HADAMARD FRACTIONAL INTEGRAL EQUATIONS AND INCLUSIONS * 215
INTRODUCTION
----
215
FUNCTIONAL PARTIAL HADAMARD FRACTIONAL INTEGRAL EQUATIONS
----
215
INTRODUCTION
----
215
MAIN RESULTS
----
216
AN EXAMPLE
----
220
FREDHOLM-TYPE HADAMARD FRACTIONAL INTEGRAL EQUATIONS
----
221
INTRODUCTION
----
221
MAIN RESULTS
----
222
AN EXAMPLE
----
229
UPPER AND LOWER SOLUTIONS METHOD FOR PARTIAL HADAMARD FRACTIONAL
INTEGRAL EQUATIONS AND INCLUSIONS
----
230
INTRODUCTION
----
230
EXISTENCE RESULTS FOR PARTIAL HADAMARD FRACTIONAL INTEGRAL
EQUATIONS
----
230
EXISTENCE RESULTS FOR PARTIAL HADAMARD FRACTIONAL INTEGRAL
INCLUSIONS
----
234
NOTES AND REMARKS
----
240
STABILITY RESULTS FOR PARTIAL HADAMARD FRACTIONAL INTEGRAL EQUATIONS AND
INCLUSIONS
----
241
INTRODUCTION
----
241
ULAM STABILITIES FOR PARTIAL HADAMARD FRACTIONAL INTEGRAL
EQUATIONS
----
241
INTRODUCTION
----
241
EXISTENCE AND ULAM STABILITIES RESULTS
----
241
AN EXAMPLE
----
246
GLOBAL STABILITY RESULTS FOR VOLTERRA-TYPE PARTIAL HADAMARD FRACTIONAL
INTEGRAL EQUATIONS
----
247
INTRODUCTION
----
247
EXISTENCE AND GLOBAL STABILITY RESULTS
----
247
AN EXAMPLE
----
254
ULAM STABILITIES FOR HADAMARD FRACTIONAL INTEGRAL EQUATIONS IN FRECHET
SPACES
----
255
INTRODUCTION
----
255
8.4.2 EXISTENCE AND ULAM STABILITIES RESULTS
----
256
8.4.3 AN EXAMPLE
-----
262
8.5 ULAM STABILITY RESULTS FOR HADAMARD PARTIAL FRACTIONAL INTEGRAL
INCLUSIONS
VIA PICARD OPERATORS
----
263
8.5.1 INTRODUCTION
----
263
8.5.2 PICARD OPERATORS THEORY
----
263
8.5.3 EXISTENCE AND ULAM STABILITY RESULTS
----
265
8.5.4 AN EXAMPLE
----
267
8.6 NOTES AND REMARKS
----
269
9 HADAMARD-STIELTJES FRACTIONAL INTEGRAL EQUATIONS * 270
9.1 INTRODUCTION
----
270
9.2 EXISTENCE AND STABILITY OF SOLUTIONS FOR HADAMARD-STIELTJES
FRACTIONAL
INTEGRAL EQUATIONS
----
271
9.2.1 INTRODUCTION
----
271
9.2.2 EXISTENCE AND ULAM STABILITIES RESULTS
----
271
9.2.3 AN EXAMPLE
----
276
9.3 GLOBAL STABILITY RESULTS FOR VOLTERRA-TYPE FRACTIONAL
HADAMARD-STIELTJES
PARTIAL INTEGRAL EQUATIONS
----
277
9.3.1 INTRODUCTION
----
277
9.3.2 EXISTENCE AND ASYMPTOTIC STABILITY RESULTS
----
277
9.3.3 AN EXAMPLE
----
285
9.4 VOLTERRA-TYPE NONLINEAR MULTIDELAY HADAMARD-STIELTJES FRACTIONAL
INTEGRAL
EQUATIONS
----
286
9.4.1 INTRODUCTION
----
286
9.4.2 EXISTENCE AND ATTRACTIVITY RESULTS
----
287
9.4.3 AN EXAMPLE
----
295
9.5 NOTES AND REMARKS
----
297
10 ULAM STABILITIES FOR RANDOM HADAMARD FRACTIONAL INTEGRAL
EQUATIONS
----
298
10.1 INTRODUCTION
----
298
10.2 PARTIAL HADAMARD FRACTIONAL INTEGRAL EQUATIONS WITH RANDOM
EFFECTS
----
299
10.2.1 INTRODUCTION
----
299
10.2.2 EXISTENCE AND ULAM STABILITIES RESULTS * 300
10.2.3 AN EXAMPLE
----
304
10.3 GLOBAL STABILITY RESULTS FOR VOLTERRA-HADAMARD RANDOM PARTIAL
FRACTIONAL
INTEGRAL EQUATIONS
----
305
10.3.1 INTRODUCTION
----
305
10.3.2 EXISTENCE OF RANDOM SOLUTIONS AND GLOBAL STABILITY RESULTS * 306
10.3.3 AN EXAMPLE
----
312
10.4 MULTIDELAY HADAMARD FRACTIONAL INTEGRAL EQUATIONS IN FRECH ET
SPACES WITH
RANDOM EFFECTS * 314
10.4.1 INTRODUCTION
----
314
10.4.2 EXISTENCE OF RANDOM SOLUTIONS AND ULAM STABILITIES RESULTS * 314
10.4.3 AN EXAMPLE
----
320
10.5 NOTES AND REMARKS
-----
321
BIBLIOGRAPHY
----
323
INDEX
----
335
|
| any_adam_object | 1 |
| author | Abbas, Saïd Benchohra, Mouffak Graef, John R. 1942- Henderson, Johnny |
| author_GND | (DE-588)1090790783 (DE-588)136868207 (DE-588)140965459 (DE-588)170788350 |
| author_facet | Abbas, Saïd Benchohra, Mouffak Graef, John R. 1942- Henderson, Johnny |
| author_role | aut aut aut aut |
| author_sort | Abbas, Saïd |
| author_variant | s a sa m b mb j r g jr jrg j h jh |
| building | Verbundindex |
| bvnumber | BV045296729 |
| classification_rvk | SK 540 SK 640 |
| ctrlnum | (OCoLC)1073147471 (DE-599)DNB1137844310 |
| dewey-full | 515.83 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.83 |
| dewey-search | 515.83 |
| dewey-sort | 3515.83 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV045296729 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T08:14:09Z |
| institution | BVB |
| institution_GND | (DE-588)10095502-2 |
| isbn | 9783110553130 3110553139 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-030683983 |
| oclc_num | 1073147471 |
| open_access_boolean | |
| owner | DE-20 |
| owner_facet | DE-20 |
| physical | XXIII, 336 Seiten 24 cm |
| publishDate | 2018 |
| publishDateSearch | 2018 |
| publishDateSort | 2018 |
| publisher | De Gruyter |
| record_format | marc |
| series | De Gruyter series in nonlinear analysis and applications |
| series2 | De Gruyter series in nonlinear analysis and applications |
| spelling | Abbas, Saïd Verfasser (DE-588)1090790783 aut Implicit fractional differential and integral equations existence and stability Saïd Abbas, Mouffak Benchohra, John R. Graef, Johnny Henderson Berlin De Gruyter [2018] XXIII, 336 Seiten 24 cm txt rdacontent n rdamedia nc rdacarrier De Gruyter series in nonlinear analysis and applications Volume 26 Gebrochene Analysis (DE-588)4722475-7 gnd rswk-swf Integralgleichung (DE-588)4027229-1 gnd rswk-swf Funktional-Differentialgleichung (DE-588)4155668-9 gnd rswk-swf Differentialgleichung Existenzsatz Gebrochene Analysis Integralgleichung Stabilität Funktional-Differentialgleichung (DE-588)4155668-9 s Integralgleichung (DE-588)4027229-1 s Gebrochene Analysis (DE-588)4722475-7 s DE-604 Benchohra, Mouffak Verfasser (DE-588)136868207 aut Graef, John R. 1942- Verfasser (DE-588)140965459 aut Henderson, Johnny Verfasser (DE-588)170788350 aut Walter de Gruyter GmbH & Co. KG (DE-588)10095502-2 pbl Elektronische Reproduktion 9783110553185 Elektronische Reproduktion 9783110553819 Erscheint auch als 9783110553826 Erscheint auch als Online-Ausgabe Abbas, Saïd Implicit Fractional Differential and Integral Equations Berlin/Boston : De Gruyter, 2018 Online-Ressourcen, 359 Seiten De Gruyter series in nonlinear analysis and applications Volume 26 (DE-604)BV005530011 26 B:DE-101 application/pdf http://d-nb.info/1137844310/04 Inhaltsverzeichnis X:MVB http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110553130&searchTitles=true DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030683983&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Abbas, Saïd Benchohra, Mouffak Graef, John R. 1942- Henderson, Johnny Implicit fractional differential and integral equations existence and stability De Gruyter series in nonlinear analysis and applications Gebrochene Analysis (DE-588)4722475-7 gnd Integralgleichung (DE-588)4027229-1 gnd Funktional-Differentialgleichung (DE-588)4155668-9 gnd |
| subject_GND | (DE-588)4722475-7 (DE-588)4027229-1 (DE-588)4155668-9 |
| title | Implicit fractional differential and integral equations existence and stability |
| title_auth | Implicit fractional differential and integral equations existence and stability |
| title_exact_search | Implicit fractional differential and integral equations existence and stability |
| title_full | Implicit fractional differential and integral equations existence and stability Saïd Abbas, Mouffak Benchohra, John R. Graef, Johnny Henderson |
| title_fullStr | Implicit fractional differential and integral equations existence and stability Saïd Abbas, Mouffak Benchohra, John R. Graef, Johnny Henderson |
| title_full_unstemmed | Implicit fractional differential and integral equations existence and stability Saïd Abbas, Mouffak Benchohra, John R. Graef, Johnny Henderson |
| title_short | Implicit fractional differential and integral equations |
| title_sort | implicit fractional differential and integral equations existence and stability |
| title_sub | existence and stability |
| topic | Gebrochene Analysis (DE-588)4722475-7 gnd Integralgleichung (DE-588)4027229-1 gnd Funktional-Differentialgleichung (DE-588)4155668-9 gnd |
| topic_facet | Gebrochene Analysis Integralgleichung Funktional-Differentialgleichung |
| url | http://d-nb.info/1137844310/04 http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110553130&searchTitles=true http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030683983&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV005530011 |
| work_keys_str_mv | AT abbassaid implicitfractionaldifferentialandintegralequationsexistenceandstability AT benchohramouffak implicitfractionaldifferentialandintegralequationsexistenceandstability AT graefjohnr implicitfractionaldifferentialandintegralequationsexistenceandstability AT hendersonjohnny implicitfractionaldifferentialandintegralequationsexistenceandstability AT walterdegruytergmbhcokg implicitfractionaldifferentialandintegralequationsexistenceandstability |
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