The analysis of fractional differential equations: an application-oriented exposition using differential operators of caputo type
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2010
|
| Schriftenreihe: | Lecture notes in mathematics
2004 |
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | Literaturangaben |
| Beschreibung: | VIII, 247 S. graph. Darst. |
| ISBN: | 9783642145735 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV036705101 | ||
| 003 | DE-604 | ||
| 005 | 20200116 | ||
| 007 | t | ||
| 008 | 101006s2010 d||| |||| 00||| eng d | ||
| 016 | 7 | |a 1003553567 |2 DE-101 | |
| 020 | |a 9783642145735 |9 978-3-642-14573-5 | ||
| 020 | |z 9783642145742 |c eISBN |9 978-3-642-14574-2 | ||
| 035 | |a (OCoLC)669792009 | ||
| 035 | |a (DE-599)DNB1003553567 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-824 |a DE-11 |a DE-83 |a DE-91G |a DE-188 |a DE-19 |a DE-862 | ||
| 082 | 0 | |a 515.35 |2 22/ger | |
| 084 | |a SI 850 |0 (DE-625)143199: |2 rvk | ||
| 084 | |a SK 500 |0 (DE-625)143243: |2 rvk | ||
| 084 | |a 34A08 |2 msc | ||
| 084 | |a 510 |2 sdnb | ||
| 084 | |a MAT 260f |2 stub | ||
| 084 | |a MAT 340f |2 stub | ||
| 100 | 1 | |a Diethelm, Kai |d 1967- |e Verfasser |0 (DE-588)113509561 |4 aut | |
| 245 | 1 | 0 | |a The analysis of fractional differential equations |b an application-oriented exposition using differential operators of caputo type |c Kai Diethelm |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2010 | |
| 300 | |a VIII, 247 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v 2004 | |
| 500 | |a Literaturangaben | ||
| 650 | 0 | 7 | |a Gebrochene Analysis |0 (DE-588)4722475-7 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Gebrochene Analysis |0 (DE-588)4722475-7 |D s |
| 689 | 0 | |5 DE-604 | |
| 830 | 0 | |a Lecture notes in mathematics |v 2004 |w (DE-604)BV000676446 |9 2004 | |
| 856 | 4 | 2 | |m X:MVB |q text/html |u http://deposit.dnb.de/cgi-bin/dokserv?id=3493220&prov=M&dok_var=1&dok_ext=htm |3 Inhaltstext |
| 856 | 4 | 2 | |m DNB Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020623440&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-020623440 | |
Datensatz im Suchindex
| DE-BY-862_location | 2000 |
|---|---|
| DE-BY-FWS_call_number | 2000/SK 500 D565 |
| DE-BY-FWS_katkey | 746334 |
| DE-BY-FWS_media_number | 083000508984 083000508999 |
| _version_ | 1824553921823113216 |
| adam_text |
CONTENTS PART I FUNDAMENTALS OF FRACTIONAL CALCULUS 1 INTRODUCTION 3 1.1
MOTIVATION 3 1.2 THE BASIC IDEA 7 1.3 AN EXAMPLE APPLICATION OF
FRACTIONAL CALCULUS 10 EXERCISES 12 2 RIEMANN-LIOUVILLE DIFFERENTIAL AND
INTEGRAL OPERATORS 13 2. 1 RIEMANN-LIOUVILLE INTEGRALS 13 2.2
RIEMANN-LIOUVILLE DERIVATIVES 26 2.3 RELATIONS BETWEEN RIEMANN-LIOUVILLE
INTEGRALS AND DERIVATIVES 39 2.4 GRUENWALD-LETNIKOV OPERATORS 41
EXERCISES 46 3 CAPUTO'S APPROACH 49 3. 1 DEFINITION AND BASIC PROPERTIES
49 3.2 NONCLASSICAL REPRESENTATIONS OF CAPUTO OPERATORS 60 EXERCISES 65
4 MITTAG-LEFFLER FUNCTIONS 67 EXERCISES 72 PART II THEORY OF FRACTIONAL
DIFFERENTIAL EQUATIONS 5 EXISTENCE AND UNIQUENESS RESULTS FOR
RIEMANN-LIOUVILLE FRACTIONAL DIFFERENTIAL EQUATIONS 77 EXERCISES 82 6
SINGLE-TERM CAPUTO FRACTIONAL DIFFERENTIAL EQUATIONS: BASIC THEORY AND
FUNDAMENTAL RESULTS 85 6. 1 EXISTENCE OF SOLUTIONS 85 6.2 UNIQUENESS OF
SOLUTIONS 93 6.3 INFLUENCEOFPERTURBEDDATA 109 BIBLIOGRAFISCHE
INFORMATIONEN HTTP://D-NB.INFO/1003553567 DIGITALISIERT DURCH 245 VIII
CONTENTS 6.4 SMOOTHNESS OF THE SOLUTIONS 116 6.5 BOUNDARY VALUE PROBLEMS
127 EXERCISES 132 7 SINGLE-TERM CAPUTO FRACTIONAL DIFFERENTIAL
EQUATIONS: ADVANCED RESULTS FOR SPECIAL CASES 133 7. 1 INITIAL VALUE
PROBLEMS FOR LINEAR EQUATIONS 133 7.2 BOUNDARY VALUE PROBLEMS FOR LINEAR
EQUATIONS 154 7.3 STABILITY OF FRACTIONAL DIFFERENTIAL EQUATIONS 157 7.4
SINGULAR EQUATIONS 163 EXERCISES 166 8 MULTI-TERM CAPUTO FRACTIONAL
DIFFERENTIAL EQUATIONS 1 67 EXERCISES 1 85 APPENDIX A LIST OF SYMBOLS
189 B A TABLE OF CAPUTO DERIVATIVES 193 C NUMERICAL SOLUTION OF
FRACTIONAL DIFFERENTIAL EQUATIONS 195 C. 1 AN ALGORITHM FOR SINGLE-TERM
EQUATIONS 195 C.2 NUMERICAL SCHEMES FOR MULTI-TERM EQUATIONS 211
EXERCISE 225 D USEFUL RESULTS FROM ANALYSIS 227 D. 1 EULER'S GAMMA
FUNCTION 227 D.2 FIXED POINT THEOREMS 229 D.3 THE LAPLACE TRANSFORM 230
D.4 HADAMARD'S FINITE-PART INTEGRAL 233 D.5 APPROXIMATION THEORY 234
EXERCISES 235 REFERENCES 237 INDEX |
| any_adam_object | 1 |
| author | Diethelm, Kai 1967- |
| author_GND | (DE-588)113509561 |
| author_facet | Diethelm, Kai 1967- |
| author_role | aut |
| author_sort | Diethelm, Kai 1967- |
| author_variant | k d kd |
| building | Verbundindex |
| bvnumber | BV036705101 |
| classification_rvk | SI 850 SK 500 |
| classification_tum | MAT 260f MAT 340f |
| ctrlnum | (OCoLC)669792009 (DE-599)DNB1003553567 |
| dewey-full | 515.35 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.35 |
| dewey-search | 515.35 |
| dewey-sort | 3515.35 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>00000nam a2200000 cb4500</leader><controlfield tag="001">BV036705101</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20200116</controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">101006s2010 d||| |||| 00||| eng d</controlfield><datafield tag="016" ind1="7" ind2=" "><subfield code="a">1003553567</subfield><subfield code="2">DE-101</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783642145735</subfield><subfield code="9">978-3-642-14573-5</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="z">9783642145742</subfield><subfield code="c">eISBN</subfield><subfield code="9">978-3-642-14574-2</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)669792009</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)DNB1003553567</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-824</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-188</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-862</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515.35</subfield><subfield code="2">22/ger</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SI 850</subfield><subfield code="0">(DE-625)143199:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 500</subfield><subfield code="0">(DE-625)143243:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">34A08</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">510</subfield><subfield code="2">sdnb</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 260f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 340f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Diethelm, Kai</subfield><subfield code="d">1967-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)113509561</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">The analysis of fractional differential equations</subfield><subfield code="b">an application-oriented exposition using differential operators of caputo type</subfield><subfield code="c">Kai Diethelm</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Berlin [u.a.]</subfield><subfield code="b">Springer</subfield><subfield code="c">2010</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">VIII, 247 S.</subfield><subfield code="b">graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Lecture notes in mathematics</subfield><subfield code="v">2004</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Literaturangaben</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Gebrochene Analysis</subfield><subfield code="0">(DE-588)4722475-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Gebrochene Analysis</subfield><subfield code="0">(DE-588)4722475-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Lecture notes in mathematics</subfield><subfield code="v">2004</subfield><subfield code="w">(DE-604)BV000676446</subfield><subfield code="9">2004</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">X:MVB</subfield><subfield code="q">text/html</subfield><subfield code="u">http://deposit.dnb.de/cgi-bin/dokserv?id=3493220&prov=M&dok_var=1&dok_ext=htm</subfield><subfield code="3">Inhaltstext</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">DNB Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020623440&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-020623440</subfield></datafield></record></collection> |
| id | DE-604.BV036705101 |
| illustrated | Illustrated |
| indexdate | 2025-02-20T06:43:34Z |
| institution | BVB |
| isbn | 9783642145735 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020623440 |
| oclc_num | 669792009 |
| open_access_boolean | |
| owner | DE-824 DE-11 DE-83 DE-91G DE-BY-TUM DE-188 DE-19 DE-BY-UBM DE-862 DE-BY-FWS |
| owner_facet | DE-824 DE-11 DE-83 DE-91G DE-BY-TUM DE-188 DE-19 DE-BY-UBM DE-862 DE-BY-FWS |
| physical | VIII, 247 S. graph. Darst. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spellingShingle | Diethelm, Kai 1967- The analysis of fractional differential equations an application-oriented exposition using differential operators of caputo type Lecture notes in mathematics Gebrochene Analysis (DE-588)4722475-7 gnd |
| subject_GND | (DE-588)4722475-7 |
| title | The analysis of fractional differential equations an application-oriented exposition using differential operators of caputo type |
| title_auth | The analysis of fractional differential equations an application-oriented exposition using differential operators of caputo type |
| title_exact_search | The analysis of fractional differential equations an application-oriented exposition using differential operators of caputo type |
| title_full | The analysis of fractional differential equations an application-oriented exposition using differential operators of caputo type Kai Diethelm |
| title_fullStr | The analysis of fractional differential equations an application-oriented exposition using differential operators of caputo type Kai Diethelm |
| title_full_unstemmed | The analysis of fractional differential equations an application-oriented exposition using differential operators of caputo type Kai Diethelm |
| title_short | The analysis of fractional differential equations |
| title_sort | the analysis of fractional differential equations an application oriented exposition using differential operators of caputo type |
| title_sub | an application-oriented exposition using differential operators of caputo type |
| topic | Gebrochene Analysis (DE-588)4722475-7 gnd |
| topic_facet | Gebrochene Analysis |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=3493220&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020623440&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT diethelmkai theanalysisoffractionaldifferentialequationsanapplicationorientedexpositionusingdifferentialoperatorsofcaputotype |
Beschreibung
THWS Schweinfurt Zentralbibliothek Lesesaal
| Signatur: |
2000 SK 500 D565 |
|---|---|
| Exemplar 1 | ausleihbar Verfügbar Bestellen |
| Exemplar 2 | ausleihbar Verfügbar Bestellen |