Introduction to fractional differential equations:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cham, Switzerland
Springer
[2019]
|
| Schriftenreihe: | Nonlinear systems and complexity
Volume 25 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xii, 188 pages Illustrationen 25 cm |
Internformat
MARC
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| 100 | 1 | |a Milici, Constantin |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Introduction to fractional differential equations |c Constantin Milici, Gheorghe Drăgănescu, J. Tenreiro Machado |
| 264 | 1 | |a Cham, Switzerland |b Springer |c [2019] | |
| 300 | |a xii, 188 pages |b Illustrationen |c 25 cm | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a Nonlinear systems and complexity |v Volume 25 | |
| 650 | 4 | |a Fractional differential equations | |
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| 650 | 0 | 7 | |a Differentialgleichung |0 (DE-588)4012249-9 |2 gnd |9 rswk-swf |
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| 700 | 1 | |a Draganescu, Gheorghe |e Verfasser |4 aut | |
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| 830 | 0 | |a Nonlinear systems and complexity |v Volume 25 |w (DE-604)BV041257000 |9 25 | |
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Datensatz im Suchindex
| _version_ | 1804179343244525568 |
|---|---|
| adam_text | Contents 1 Special Functions .......................................................................................... 1.1 Euler’s Function....................................................................................... 1.1.1 Gamma Function........................................................................ 1.1.2 Beta Function............................................................................. 1.2 Integral Functions.................................................................................... 1.3 Mittag-Leffler Function.......................................................................... 1.4 Function E(t, a, a)................................................................................. References........................................................................................................ 1 1 1 7 11 11 13 14 2 Fractional Derivative and Fractional Integral......................................... 2.1 Fractional Integral and Derivative......................................................... References........................................................................................................ 17 17 31 3 The Laplace Transform................................................................................ 3.1 Calculus of the Images........................................................................... 3.2 Calculus of the Original Function......................................................... 3.2.1 Calculus of Original Using Residues...................................... 3.2.2 Calculus of Original with Post’s
Inversion Formula.............. 3.3 The Properties of the Laplace Transform............................................. 3.3.1 The Property of Linearity ......................................................... 3.3.2 Similarity Theorem................................................................... 3.3.3 The Differentiation and Integration Theorems....................... 3.3.4 Delay Theorem........................................................................... 3.3.5 Displacement Theorem............................................................. 3.3.6 Multiplication Theorem............................................................ 3.3.7 Properties of the Inverse Laplace Transform.......................... 3.4 Laplace Transform of the Fractional Integrals and Derivatives......... 3.4.1 Fractional Integrals................................................................... 3.4.2 Fractional Derivatives............................................................... References........................................................................................................ 33 34 35 35 36 37 37 37 37 39 39 39 39 43 43 43 45 xi
xii 4 Contents Fractional Differential Equations........................................................... 4.1 The Existence and Uniqueness Theorem for Initial Value Problems............................................................................................. 4.2 Linear Fractional Differential Equations........................................... 4.3 Nonlinear Equations.......................................................................... 4.3.1 The Adomian Decomposition Method................................... 4.3.2 Decomposition of Nonlinear Equations ................................ 4.3.3 Perturbation Method.............................................................. 4.4 Fractional Systems of Differential Equations.................................... 4.4.1 Linear Systems....................................................................... 4.4.2 Nonlinear Systems................................................................. References.................................................................................................. 47 Generalized Systems................................................................................. 5.1 Cornu Fractional System.................................................................. 5.1.1 Cos and Sin Fractional of Type Fresnel ................................ 5.1.2 Cornu Fractional System and Curve...................................... 5.1.3 Cornu Generalized Curve/System ......................................... 5.1.4 Cornu Fractional System in a Plane....................................... 5.1.5 Fractional
Cornu Spiral on the Sphere................................... 5.1.6 Fractional Cornu Spiral on the Cone...................................... 5.2 Power Series....................................................................................... 5.2.1 The Müntz Theorem............................................................ 5.2.2 Lane-Emden Equation........................................................... 5.2.3 The Taylor Series Method..................................................... 5.2.4 The Generalized Flermite Equation....................................... 5.2.5 The Generalized Legendre Equation...................................... 5.2.6 The Generalized Bessel Equation.......................................... 5.2.7 Nonlinear Systems................................................................. References.................................................................................................. 87 87 87 88 90 90 91 93 94 94 104 108 110 Ill 113 116 120 6 Numerical Methods.................................................................................. 6.1 Variational Iteration Method for Fractional Differential Equations .. 6.2 The Least Squares Method................................................................ 6.3 The Galerkin Method for Fractional Differential Equations............. 6.4 Euler’s Method................................................................................... 6.5 Runge-Kutta Methods for Fractional Differential Equation............. 6.5.1 The Second Order Runge-Kutta Method.............................. 6.5.2 The Fourth
Order Runge-Kutta Method................................ 6.5.3 A More General System........................................................ 6.5.4 A Vectorial Runge-Kutta Algorithm .................................... References.................................................................................................. 121 121 124 135 143 149 150 153 170 179 185 5 47 54 64 64 67 75 80 80 80 85 Index................................................................................................................. 187
|
| any_adam_object | 1 |
| author | Milici, Constantin Draganescu, Gheorghe Machado, José António Tenreiro 1957- |
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| bvnumber | BV045448150 |
| classification_rvk | SK 500 |
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| discipline | Mathematik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-10T08:18:21Z |
| institution | BVB |
| language | English |
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| physical | xii, 188 pages Illustrationen 25 cm |
| publishDate | 2019 |
| publishDateSearch | 2019 |
| publishDateSort | 2019 |
| publisher | Springer |
| record_format | marc |
| series | Nonlinear systems and complexity |
| series2 | Nonlinear systems and complexity |
| spelling | Milici, Constantin Verfasser aut Introduction to fractional differential equations Constantin Milici, Gheorghe Drăgănescu, J. Tenreiro Machado Cham, Switzerland Springer [2019] xii, 188 pages Illustrationen 25 cm txt rdacontent n rdamedia nc rdacarrier Nonlinear systems and complexity Volume 25 Fractional differential equations Differentialrechnung (DE-588)4012252-9 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Differentialrechnung (DE-588)4012252-9 s Differentialgleichung (DE-588)4012249-9 s DE-604 Draganescu, Gheorghe Verfasser aut Machado, José António Tenreiro 1957- Verfasser (DE-588)1030244308 aut Erscheint auch als Online-Ausgabe 978-3-030-00895-6 Nonlinear systems and complexity Volume 25 (DE-604)BV041257000 25 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030833583&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Milici, Constantin Draganescu, Gheorghe Machado, José António Tenreiro 1957- Introduction to fractional differential equations Nonlinear systems and complexity Fractional differential equations Differentialrechnung (DE-588)4012252-9 gnd Differentialgleichung (DE-588)4012249-9 gnd |
| subject_GND | (DE-588)4012252-9 (DE-588)4012249-9 |
| title | Introduction to fractional differential equations |
| title_auth | Introduction to fractional differential equations |
| title_exact_search | Introduction to fractional differential equations |
| title_full | Introduction to fractional differential equations Constantin Milici, Gheorghe Drăgănescu, J. Tenreiro Machado |
| title_fullStr | Introduction to fractional differential equations Constantin Milici, Gheorghe Drăgănescu, J. Tenreiro Machado |
| title_full_unstemmed | Introduction to fractional differential equations Constantin Milici, Gheorghe Drăgănescu, J. Tenreiro Machado |
| title_short | Introduction to fractional differential equations |
| title_sort | introduction to fractional differential equations |
| topic | Fractional differential equations Differentialrechnung (DE-588)4012252-9 gnd Differentialgleichung (DE-588)4012249-9 gnd |
| topic_facet | Fractional differential equations Differentialrechnung Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030833583&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV041257000 |
| work_keys_str_mv | AT miliciconstantin introductiontofractionaldifferentialequations AT draganescugheorghe introductiontofractionaldifferentialequations AT machadojoseantoniotenreiro introductiontofractionaldifferentialequations |