q-fractional calculus and equations:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2012
|
| Series: | Lecture notes in mathematics
2056 |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Item Description: | Literaturverz.: S. 303 - 314 |
| Physical Description: | XIX, 318 S. graph. Darst. 235 mm x 155 mm |
| ISBN: | 9783642308970 |
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MARC
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| 100 | 1 | |a Annaby, Mahmoud H. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a q-fractional calculus and equations |c Mahmoud H. Annaby ; Zeinab S. Mansour |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2012 | |
| 300 | |a XIX, 318 S. |b graph. Darst. |c 235 mm x 155 mm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Lecture notes in mathematics |v 2056 | |
| 500 | |a Literaturverz.: S. 303 - 314 | ||
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| 700 | 1 | |a Mansour, Zeinab S. |e Verfasser |4 aut | |
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Record in the Search Index
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| adam_text |
IMAGE 1
CONTENTS
1 PRELIMINARIES 1
1.1 S O M E CLASSICAL RESULTS 1
1.2 G-NOTATIONS AND RESULTS 3
1.3 T H E ^-DIFFERENCE OPERATOR 5
1.3.1 M O R E PROPERTIES O F ^-INTEGRALS 9
1.4 FUNCTION SPACES 14
1.5 S O M E ^-FUNCTIONS 19
1.6 T H E G - G A M M A AND G-BETA FUNCTIONS 2 2
1.7 ^-INTEGRAL REPRESENTATIONS O F THE Q - G A M M A , G-BETA AND S O M
E RELATED ^-FUNCTIONS 2 5
1.8 ^-ANALOGUE O F THE WRIGHT FUNCTION 2 8
1.9 ^-ANALOGUES O F THE LAPLACE TRANSFORM 3 0
1.9.1 T H E Q L S T R A N S F O R M 3 0
1.9.2 T H E Q T R A N S F O R M 3 3
1.10 ^-ANALOGUE O F THE MELLIN TRANSFORM 3 6
2 Q -DIFFERENCE EQUATIONS 41
2.1 INTRODUCTION 4 1
2.2 ^-SUCCESSIVE APPROXIMATIONS 4 3
2.3 ^-INITIAL VALUE PROBLEMS IN A NEIGHBORHOOD O F ZERO 4 6
2.4 T H E PROBLEM IN A NEIGHBORHOOD O F INFINITY 5 3
2.5 LINEAR ^-DIFFERENCE EQUATIONS 5 7
2.6 A FUNDAMENTAL SET O F SOLUTION 5 8
2.7 A G-TYPE WRONSKIAN 6 0
2.8 ZEROS O F ^-FUNCTIONS 6 7
3 QR -STURM-LIOUVILLE PROBLEMS 7 3
3.1 INTRODUCTION 7 3
3.2 JR-STURM-LIOUVILLE PROBLEM 7 5
3.2.1 T H E SELF ADJOINT PROBLEM 7 9
3.3 BASIC GREEN'S FUNCTION 85
3.4 EIGENFUNCTIONS EXPANSION FORMULA 9 0
XIII
HTTP://D-NB.INFO/1022401548
IMAGE 2
XIV C O N T E N T S
3.5 G 2-ANALOGUE O F THE FOURIER TRANSFORM 9 7
3.6 A REFORMULATION O F THE (/ 2-FOURIER TRANSFORM 101
4 RIEMANN-LIOUVILLE 7-FRACTIONAL CALCULI 107
4.1 CLASSICAL FRACTIONAL CALCULI 107
4.2 RECENT HISTORY O F FRACTIONAL (/-CALCULUS 113
4.2.1 T H E TIME SCALE FRACTIONAL (/-CALCULUS 117
4.3 Y-ABEL INTEGRAL EQUATION 118
4.4 S O M E PROPERTIES O F (/-RIEMANN-LIOUVILLE FRACTIONAL INTEGRAL
OPERATOR 125
4.5 (/-RIEMANN-LIOUVILLE FRACTIONAL CALCULUS 132
4.6 A COMPLEX VARIABLE APPROACH FOR RIEMANN-LIOUVILLE FRACTIONAL
(/-DERIVATIVE 138
4.7 T H E LAW O F EXPONENTS 143
4.8 MISCELLANEOUS EXAMPLES 144
5 OTHER Q -FRACTIONAL CALCULI 147
5.1 BASIC GRIINWALD-LETNIKOV FRACTIONAL DERIVATIVE 147
5.2 CAPUTO FRACTIONAL (/-DERIVATIVE 148
5.3 ERDELI-KOBER FRACTIONAL (/-INTEGRAL OPERATOR 153
5.4 WEYL FRACTIONAL (/-CALCULUS 156
5.5 FRACTIONAL (/-OPERATOR AS A GENERALIZATION O F A RIGHT INVERSE O F
ASKEY-WILSON OPERATOR 160
5.6 FRACTIONAL (/-OPERATOR AS A GENERALIZATION O F A (/-DIFFERENCE
OPERATOR 162
6 FRACTIONAL ^-LEIBNIZ RULE AND APPLICATIONS 175
6.1 LEIBNIZ RULE FOR FRACTIONAL DERIVATIVES 175
6.2 AL-SALAM-VERMA FRACTIONAL (/-LEIBNIZ FORMULA 176
6.3 (/-TAYLOR AND INTERPOLATION SERIES 177
6.3.1 A FRACTIONAL (/-TAYLOR FORMULA 179
6.4 ANALYTIC PROOFS AND APPLICATIONS 181
6.5 A GENERALIZATION FOR AGARWAL'S FRACTIONAL (/-LEIBNIZ FORMULA 183
6.6 A (/-EXTENSION O F THE LEIBNIZ RULE VIA WEYL (/-FRACTIONAL
DERIVATIVE 187
6.7 APPLICATIONS 191
7 7-MITTAG-LEFFLER FUNCTIONS 201
7.1 MITTAG-LEFFLER FUNCTIONS 201
7.2 T H E (/-MITTAG-LEFFLER FUNCTION E A,P(Z',Q) 2 0 3
7.2.1 APPLICATION O F THE Q L S T R A N S F O R M 204
7.3 T H E (/-MITTAG-LEFFLER FUNCTION E A,P(Z',Q) 204
7.4 (/-MELLIN-BARNES CONTOUR INTEGRALS FOR THE (/-MITTAG-LEFFLER
FUNCTIONS 207
7.4.1 A (/-MELLIN-BARNES CONTOUR INTEGRAL O F E A.P(Z\ Q ) 2 0 8
7.4.2 A (/-MELLIN-BARNES CONTOUR INTEGRAL O F E A_P{Z\ Q ) 2 1 0
IMAGE 3
C O N T E N T S X V
7.5 HANKEL CONTOUR INTEGRAL REPRESENTATION
O F (/-MITTAG-LEFFLER FUNCTIONS 211
7.6 (/-VOLTERRA INTEGRAL EQUATIONS 2 1 3
7.7 ZEROS O F (/-MITTAG-LEFFLER FUNCTIONS 2 2 0
8 FRACTIONAL ^-DIFFERENCE EQUATIONS 2 2 3
8.1 EQUATIONS WITH THE RIEMANN-LIOUVILLE FRACTIONAL (/-DERIVATIVES . . .
2 2 3 8.1.1 SOLUTIONS IN THE SPACE [0,] 2 2 3
8.1.2 SOLUTIONS IN THE SPACE O F WEIGHTED CONTINUOUS FUNCTIONS 227
8.2 G-RIEMANN-LIOUVILLE FRACTIONAL ORDER SYSTEMS 231
8.3 EQUATIONS WITH CAPUTO FRACTIONAL (/-DERIVATIVES 241
8.4 (/-CAPUTO FRACTIONAL ORDER SYSTEMS 2 4 5
8.5 A G-CAUCHY FRACTIONAL PROBLEM 2 5 0
8.6 LINEAR SEQUENTIAL RIEMANN-LIOUVILLE FRACTIONAL (/-DIFFERENCE
EQUATIONS 2 5 8
8.7 LINEAR SEQUENTIAL CAPUTO FRACTIONAL (/-DIFFERENCE EQUATIONS 2 6 3
8.8 FUNDAMENTAL SET O F SOLUTIONS O F A LINEAR SEQUENTIAL
RIEMANN-LIOUVILLE FRACTIONAL (/-DIFFERENCE EQUATION 2 6 6
8.9 FUNDAMENTAL SET O F SOLUTIONS O F A LINEAR SEQUENTIAL CAPUTO
FRACTIONAL (/-DIFFERENCE EQUATION 2 6 9
9 QR -INTEGRAL TRANSFORMS FOR SOLVING FRACTIONAL Q-DIFFERENCE EQUATIONS
27 1
9.1 (/-LAPLACE TRANSFORM O F FRACTIONAL (/-INTEGRALS AND (/-DERIVATIVES
271
9.2 A GENERAL SOLUTION O F NONHOMOGENEOUS LINEAR FRACTIONAL
(/-DIFFERENCE EQUATIONS 274
9.3 SOLUTIONS O F NONHOMOGENEOUS LINEAR SEQUENTIAL EQUATION 2 7 9
9.4 (/-LAPLACE TRANSFORM METHOD FOR SOLVING CERTAIN (/-INTEGRAL
EQUATIONS 2 8 2
9.5 (/-MELLIN TRANSFORM O F RIEMANN-LIOUVILLE AND WEYL FRACTIONAL
(/-DERIVATIVES 284
9.5.1 (/-MELLIN TRANSFORM METHOD FOR SOLVING NONHOMOGENEOUS FRACTIONAL
(/-DIFFERENCE EQUATION 2 8 6 9.5.2 EQUATION WITH RIEMANN-LIOUVILLE
FRACTIONAL (/-DERIVATIVE 2 8 8
9.5.3 EQUATION WITH WEYL FRACTIONAL (/-DERIVATIVE 2 8 9
9.6 (/ 2-FOURIER TRANSFORM METHOD FOR SOLVING FRACTIONAL (/-DIFFERENCE
EQUATIONS 291
A TABLES O F FRACTIONAL DERIVATIVES AND ^-DERIVATIVES 2 9 5
A . L TABLE O F RIEMANN-LIOUVILLE FRACTIONAL DERIVATIVES 2 9 5
A.2 TABLE O F RIEMANN-LIOUVILLE FRACTIONAL (/-DERIVATIVES 2 9 6
IMAGE 4
XVI C O N T E N T S
A.3 TABLE O F THE ERDELI-KOBER FRACTIONAL (/-INTEGRAL OPERATOR 2 9 6
A.4 TABLE O F ERDELI-SNEDDON (/-FRACTIONAL INTEGRAL OPERATOR 2 9 8
A.5 TABLE O F CAPUTO FRACTIONAL (/-DERIVATIVES 2 9 8
A.6 THE 1 / 2 RIEMANN-LIOUVILLE FRACTIONAL ^-DERIVATIVES 2 9 9
A.7 GENERALIZED RODRIGUES ?-TYPE FORMULAE 3 0 0
REFERENCES 3 0 3
AUTHOR INDEX 315
SUBJECT INDEX 317 |
| any_adam_object | 1 |
| author | Annaby, Mahmoud H. Mansour, Zeinab S. |
| author_facet | Annaby, Mahmoud H. Mansour, Zeinab S. |
| author_role | aut aut |
| author_sort | Annaby, Mahmoud H. |
| author_variant | m h a mh mha z s m zs zsm |
| building | Verbundindex |
| bvnumber | BV040447837 |
| classification_rvk | SI 850 |
| ctrlnum | (OCoLC)811404376 (DE-599)DNB1022401548 |
| dewey-full | 510 515 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics 515 - Analysis |
| dewey-raw | 510 515 |
| dewey-search | 510 515 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| isbn | 9783642308970 |
| language | English |
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| physical | XIX, 318 S. graph. Darst. 235 mm x 155 mm |
| publishDate | 2012 |
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| publisher | Springer |
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| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Annaby, Mahmoud H. Verfasser aut q-fractional calculus and equations Mahmoud H. Annaby ; Zeinab S. Mansour Berlin [u.a.] Springer 2012 XIX, 318 S. graph. Darst. 235 mm x 155 mm txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 2056 Literaturverz.: S. 303 - 314 q-Operator (DE-588)4380779-3 gnd rswk-swf Gebrochene Analysis (DE-588)4722475-7 gnd rswk-swf q-Operator (DE-588)4380779-3 s Gebrochene Analysis (DE-588)4722475-7 s DE-604 Mansour, Zeinab S. Verfasser aut Erscheint auch als Online-Ausgabe 978-3-642-30898-7 Lecture notes in mathematics 2056 (DE-604)BV000676446 2056 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=4040578&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025295548&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Annaby, Mahmoud H. Mansour, Zeinab S. q-fractional calculus and equations Lecture notes in mathematics q-Operator (DE-588)4380779-3 gnd Gebrochene Analysis (DE-588)4722475-7 gnd |
| subject_GND | (DE-588)4380779-3 (DE-588)4722475-7 |
| title | q-fractional calculus and equations |
| title_auth | q-fractional calculus and equations |
| title_exact_search | q-fractional calculus and equations |
| title_full | q-fractional calculus and equations Mahmoud H. Annaby ; Zeinab S. Mansour |
| title_fullStr | q-fractional calculus and equations Mahmoud H. Annaby ; Zeinab S. Mansour |
| title_full_unstemmed | q-fractional calculus and equations Mahmoud H. Annaby ; Zeinab S. Mansour |
| title_short | q-fractional calculus and equations |
| title_sort | q fractional calculus and equations |
| topic | q-Operator (DE-588)4380779-3 gnd Gebrochene Analysis (DE-588)4722475-7 gnd |
| topic_facet | q-Operator Gebrochene Analysis |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=4040578&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=025295548&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
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