Basic theory of fractional differential equations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
[Hackensack] New Jersey
World Scientific
2014
|
| Subjects: | |
| Online Access: | TUM01 Volltext |
| Item Description: | Print version record |
| Physical Description: | 1 online resource |
| ISBN: | 9789814579902 9814579904 9789814579896 9814579890 |
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MARC
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| 505 | 8 | |a 1. Preliminaries. 1.1. Introduction. 1.2. Some notations, concepts and lemmas. 1.3. Fractional calculus. 1.4. Some Results from Nonlinear Analysis. 1.5. Semigroups -- 2. Fractional functional differential equations. 2.1. Introduction. 2.2. Neutral equations with bounded delay. 2.3. p-type neutral equations. 2.4. Neutral equations with infinite delay. 2.5. Iterative functional differential equations. 2.6. Notes and remarks -- 3. Fractional ordinary differential equations in Banach spaces. 3.1. Introduction. 3.2. Cauchy problems via measure of noncompactness method. 3.3. Cauchy problems via topological degree method. 3.4. Cauchy problems via Picard operators technique. 3.5. Notes and remarks -- 4. Fractional abstract evolution equations. 4.1. Introduction. 4.2. Evolution equations with Riemann-Liouville derivative. 4.3. Evolution equations with Caputo derivative. 4.4. Nonlocal Cauchy problems for evolution equations. 4.5. Abstract Cauchy problems with almost sectorial operators. 4.6. Notes and remarks -- 5. Fractional boundary value problems via critical point theory. 5.1. Introduction. 5.2. Existence of solution for BVP with left and right fractional integrals. 5.3. Multiple solutions for BVP with parameters. 5.4. Infinite solutions for BVP with left and right fractional integrals. 5.5. Existence of solutions for BVP with left and right fractional derivatives. 5.6. Notes and remarks -- 6. Fractional partial differential equations. 6.1. Introduction. 6.2. Fractional Euler-Lagrange equations. 6.3. Time-fractional diffusion equations. 6.4. Fractional Hamiltonian systems. 6.5. Fractional Schrodinger equations. 6.6. Notes and remarks | |
| 505 | 8 | |a This invaluable book is devoted to a rapidly developing area on the research of the qualitative theory of fractional differential equations. It is self-contained and unified in presentation, and provides readers the necessary background material required to go further into the subject and explore the rich research literature. The tools used include many classical and modern nonlinear analysis methods such as fixed point theory, measure of noncompactness method, topological degree method, the Picard operators technique, critical point theory and semigroups theory. Based on research work carried | |
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Record in the Search Index
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| author_GND | (DE-588)1062995449 |
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| contents | 1. Preliminaries. 1.1. Introduction. 1.2. Some notations, concepts and lemmas. 1.3. Fractional calculus. 1.4. Some Results from Nonlinear Analysis. 1.5. Semigroups -- 2. Fractional functional differential equations. 2.1. Introduction. 2.2. Neutral equations with bounded delay. 2.3. p-type neutral equations. 2.4. Neutral equations with infinite delay. 2.5. Iterative functional differential equations. 2.6. Notes and remarks -- 3. Fractional ordinary differential equations in Banach spaces. 3.1. Introduction. 3.2. Cauchy problems via measure of noncompactness method. 3.3. Cauchy problems via topological degree method. 3.4. Cauchy problems via Picard operators technique. 3.5. Notes and remarks -- 4. Fractional abstract evolution equations. 4.1. Introduction. 4.2. Evolution equations with Riemann-Liouville derivative. 4.3. Evolution equations with Caputo derivative. 4.4. Nonlocal Cauchy problems for evolution equations. 4.5. Abstract Cauchy problems with almost sectorial operators. 4.6. Notes and remarks -- 5. Fractional boundary value problems via critical point theory. 5.1. Introduction. 5.2. Existence of solution for BVP with left and right fractional integrals. 5.3. Multiple solutions for BVP with parameters. 5.4. Infinite solutions for BVP with left and right fractional integrals. 5.5. Existence of solutions for BVP with left and right fractional derivatives. 5.6. Notes and remarks -- 6. Fractional partial differential equations. 6.1. Introduction. 6.2. Fractional Euler-Lagrange equations. 6.3. Time-fractional diffusion equations. 6.4. Fractional Hamiltonian systems. 6.5. Fractional Schrodinger equations. 6.6. Notes and remarks This invaluable book is devoted to a rapidly developing area on the research of the qualitative theory of fractional differential equations. It is self-contained and unified in presentation, and provides readers the necessary background material required to go further into the subject and explore the rich research literature. The tools used include many classical and modern nonlinear analysis methods such as fixed point theory, measure of noncompactness method, topological degree method, the Picard operators technique, critical point theory and semigroups theory. Based on research work carried |
| ctrlnum | (OCoLC)883632064 (DE-599)BVBBV043026661 |
| dewey-full | 515/.352 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.352 |
| dewey-search | 515/.352 |
| dewey-sort | 3515 3352 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| spelling | Zhou, Yong 1964- Verfasser (DE-588)1062995449 aut Basic theory of fractional differential equations by Yong Zhou (Xiangtan University, China) [Hackensack] New Jersey World Scientific 2014 1 online resource txt rdacontent c rdamedia cr rdacarrier Print version record 1. Preliminaries. 1.1. Introduction. 1.2. Some notations, concepts and lemmas. 1.3. Fractional calculus. 1.4. Some Results from Nonlinear Analysis. 1.5. Semigroups -- 2. Fractional functional differential equations. 2.1. Introduction. 2.2. Neutral equations with bounded delay. 2.3. p-type neutral equations. 2.4. Neutral equations with infinite delay. 2.5. Iterative functional differential equations. 2.6. Notes and remarks -- 3. Fractional ordinary differential equations in Banach spaces. 3.1. Introduction. 3.2. Cauchy problems via measure of noncompactness method. 3.3. Cauchy problems via topological degree method. 3.4. Cauchy problems via Picard operators technique. 3.5. Notes and remarks -- 4. Fractional abstract evolution equations. 4.1. Introduction. 4.2. Evolution equations with Riemann-Liouville derivative. 4.3. Evolution equations with Caputo derivative. 4.4. Nonlocal Cauchy problems for evolution equations. 4.5. Abstract Cauchy problems with almost sectorial operators. 4.6. Notes and remarks -- 5. Fractional boundary value problems via critical point theory. 5.1. Introduction. 5.2. Existence of solution for BVP with left and right fractional integrals. 5.3. Multiple solutions for BVP with parameters. 5.4. Infinite solutions for BVP with left and right fractional integrals. 5.5. Existence of solutions for BVP with left and right fractional derivatives. 5.6. Notes and remarks -- 6. Fractional partial differential equations. 6.1. Introduction. 6.2. Fractional Euler-Lagrange equations. 6.3. Time-fractional diffusion equations. 6.4. Fractional Hamiltonian systems. 6.5. Fractional Schrodinger equations. 6.6. Notes and remarks This invaluable book is devoted to a rapidly developing area on the research of the qualitative theory of fractional differential equations. It is self-contained and unified in presentation, and provides readers the necessary background material required to go further into the subject and explore the rich research literature. The tools used include many classical and modern nonlinear analysis methods such as fixed point theory, measure of noncompactness method, topological degree method, the Picard operators technique, critical point theory and semigroups theory. Based on research work carried Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Gebrochene Analysis (DE-588)4722475-7 gnd rswk-swf Ableitung gebrochener Ordnung (DE-588)4365956-1 gnd rswk-swf Gebrochene Analysis (DE-588)4722475-7 s DE-604 Differentialgleichung (DE-588)4012249-9 s Ableitung gebrochener Ordnung (DE-588)4365956-1 s 1\p DE-604 Erscheint auch als Druck-Ausgabe Zhou, Yong, 1964- Basic theory of fractional differential equations http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=810391 Aggregator Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Zhou, Yong 1964- Basic theory of fractional differential equations 1. Preliminaries. 1.1. Introduction. 1.2. Some notations, concepts and lemmas. 1.3. Fractional calculus. 1.4. Some Results from Nonlinear Analysis. 1.5. Semigroups -- 2. Fractional functional differential equations. 2.1. Introduction. 2.2. Neutral equations with bounded delay. 2.3. p-type neutral equations. 2.4. Neutral equations with infinite delay. 2.5. Iterative functional differential equations. 2.6. Notes and remarks -- 3. Fractional ordinary differential equations in Banach spaces. 3.1. Introduction. 3.2. Cauchy problems via measure of noncompactness method. 3.3. Cauchy problems via topological degree method. 3.4. Cauchy problems via Picard operators technique. 3.5. Notes and remarks -- 4. Fractional abstract evolution equations. 4.1. Introduction. 4.2. Evolution equations with Riemann-Liouville derivative. 4.3. Evolution equations with Caputo derivative. 4.4. Nonlocal Cauchy problems for evolution equations. 4.5. Abstract Cauchy problems with almost sectorial operators. 4.6. Notes and remarks -- 5. Fractional boundary value problems via critical point theory. 5.1. Introduction. 5.2. Existence of solution for BVP with left and right fractional integrals. 5.3. Multiple solutions for BVP with parameters. 5.4. Infinite solutions for BVP with left and right fractional integrals. 5.5. Existence of solutions for BVP with left and right fractional derivatives. 5.6. Notes and remarks -- 6. Fractional partial differential equations. 6.1. Introduction. 6.2. Fractional Euler-Lagrange equations. 6.3. Time-fractional diffusion equations. 6.4. Fractional Hamiltonian systems. 6.5. Fractional Schrodinger equations. 6.6. Notes and remarks This invaluable book is devoted to a rapidly developing area on the research of the qualitative theory of fractional differential equations. It is self-contained and unified in presentation, and provides readers the necessary background material required to go further into the subject and explore the rich research literature. The tools used include many classical and modern nonlinear analysis methods such as fixed point theory, measure of noncompactness method, topological degree method, the Picard operators technique, critical point theory and semigroups theory. Based on research work carried Differentialgleichung (DE-588)4012249-9 gnd Gebrochene Analysis (DE-588)4722475-7 gnd Ableitung gebrochener Ordnung (DE-588)4365956-1 gnd |
| subject_GND | (DE-588)4012249-9 (DE-588)4722475-7 (DE-588)4365956-1 |
| title | Basic theory of fractional differential equations |
| title_auth | Basic theory of fractional differential equations |
| title_exact_search | Basic theory of fractional differential equations |
| title_full | Basic theory of fractional differential equations by Yong Zhou (Xiangtan University, China) |
| title_fullStr | Basic theory of fractional differential equations by Yong Zhou (Xiangtan University, China) |
| title_full_unstemmed | Basic theory of fractional differential equations by Yong Zhou (Xiangtan University, China) |
| title_short | Basic theory of fractional differential equations |
| title_sort | basic theory of fractional differential equations |
| topic | Differentialgleichung (DE-588)4012249-9 gnd Gebrochene Analysis (DE-588)4722475-7 gnd Ableitung gebrochener Ordnung (DE-588)4365956-1 gnd |
| topic_facet | Differentialgleichung Gebrochene Analysis Ableitung gebrochener Ordnung |
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| work_keys_str_mv | AT zhouyong basictheoryoffractionaldifferentialequations |