Verfügbarkeit: Implicit fractional differential and integral equations

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Titel:	Implicit fractional differential and integral equations existence and stability
Von:	Saïd Abbas, Mouffak Benchohra, John R. Graef, Johnny Henderson
Person:	Abbas, Saïd Verfasser aut Benchohra, Mouffak Graef, John R. Henderson, Johnny 1942-
Hauptverfassende:	Abbas, Saïd (VerfasserIn), Benchohra, Mouffak (VerfasserIn), Graef, John R. 1942- (VerfasserIn), Henderson, Johnny (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Berlin De Gruyter [2018]
Schriftenreihe:	De Gruyter series in nonlinear analysis and applications Volume 26
Schlagworte:	Gebrochene Analysis Integralgleichung Funktional-Differentialgleichung Differentialgleichung Existenzsatz Stabilität
Online-Zugang:	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
Beschreibung:	XXIII, 336 Seiten 24 cm
ISBN:	9783110553130 3110553139

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Datensatz im Suchindex

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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
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record_format	marc
series	De Gruyter series in nonlinear analysis and applications
series2	De Gruyter series in nonlinear analysis and applications
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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