The analysis of fractional differential equations: an application-oriented exposition using differential operators of caputo type
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2010
|
| Series: | Lecture notes in mathematics
2004 |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Item Description: | Literaturangaben |
| Physical Description: | VIII, 247 S. graph. Darst. |
| ISBN: | 9783642145735 |
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| 245 | 1 | 0 | |a The analysis of fractional differential equations |b an application-oriented exposition using differential operators of caputo type |c Kai Diethelm |
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Record in the Search Index
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| 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 |
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| author | Diethelm, Kai 1967- |
| author_GND | (DE-588)113509561 |
| author_facet | Diethelm, Kai 1967- |
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| 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 |
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| indexdate | 2025-02-20T06:43:34Z |
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| isbn | 9783642145735 |
| language | English |
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| 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 |
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Description
THWS Schweinfurt Zentralbibliothek Lesesaal
| Call Number: |
2000 SK 500 D565 |
|---|---|
| Copy 1 | ausleihbar Available Place a Hold |
| Copy 2 | ausleihbar Available Place a Hold |