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Fractional calculus [[electronic resource] ] : models and numerical methods / / Dumitru Baleanu ... [et al.]
| Fractional calculus [[electronic resource] ] : models and numerical methods / / Dumitru Baleanu ... [et al.] |
| Autore | Baleanu D (Dumitru) |
| Pubbl/distr/stampa | Singapore, : World Scientific Pub. Co., 2012 |
| Descrizione fisica | 1 online resource (426 p.) |
| Disciplina | 515.83 |
| Collana | Series on complexity, nonlinearity and chaos |
| Soggetto topico |
Fractional calculus
Mathematical models |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-280-66952-7
9786613646453 981-4355-21-6 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Contents; Preface; 1. Preliminaries; 1.1 Fourier and Laplace Transforms; 1.2 Special Functions and Their Properties; 1.2.1 The Gamma function and related special functions; 1.2.2 Hypergeometric functions; 1.2.3 Mittag-Leffler functions; 1.3 Fractional Operators; 1.3.1 Riemann-Liouville fractional integrals and fractional derivatives; 1.3.2 Caputo fractional derivatives; 1.3.3 Liouville fractional integrals and fractional derivatives. Marchaud derivatives; 1.3.4 Generalized exponential functions; 1.3.5 Hadamard type fractional integrals and fractional derivatives
1.3.6 Fractional integrals and fractional derivatives of a function with respect to another function1.3.7 Grunwald-Letnikov fractional derivatives; 2. A Survey of Numerical Methods for the Solution of Ordinary and Partial Fractional Differential Equations; 2.1 Approximation of Fractional Operators; 2.1.1 Methods based on quadrature theory; 2.1.2 Grunwald-Letnikov methods; 2.1.3 Lubich's fractional linear multistep methods; 2.2 Direct Methods for Fractional ODEs; 2.2.1 The basic idea; 2.2.2 Quadrature-based direct methods; 2.3 Indirect Methods for Fractional ODEs; 2.3.1 The basic idea 2.3.2 An Adams-type predictor-corrector method2.3.3 The Cao-Burrage-Abdullah approach; 2.4 Linear Multistep Methods; 2.5 Other Methods; 2.6 Methods for Terminal Value Problems; 2.7 Methods for Multi-Term FDE and Multi-Order FDS; 2.8 Extension to Fractional PDEs; 2.8.1 General formulation of the problem; 2.8.2 Examples; 3. Efficient Numerical Methods; 3.1 Methods for Ordinary Differential Equations; 3.1.1 Dealing with non-locality; 3.1.2 Parallelization of algorithms; 3.1.3 When and when not to use fractional linear multistep formulas; 3.1.4 The use of series expansions 3.1.5 Adams methods for multi-order equations3.1.6 Two classes of singular equations as application examples; 3.2 Methods for Partial Differential Equations; 3.2.1 The method of lines; 3.2.2 BDFs for time-fractional equations; 3.2.3 Other methods; 3.2.4 Methods for equations with space-fractional operators; 4. Generalized Stirling Numbers and Applications; 4.1 Introduction; 4.2 Stirling Functions s(a, k), a C; 4.2.1 Equivalent definitions; 4.2.2 Multiple sum representations. The Riemann Zeta function; 4.3 General Stirling Functions s(α, β) with Complex Arguments 4.3.1 Definition and main result4.3.2 Differentiability of the s(α, β); The zeta function encore; 4.3.3 Recurrence relations for s(α, β); 4.4 Stirling Functions of the Second Kind S(α, k); 4.4.1 Stirling functions S(a, k), a 0, and their representations by Liouville and Marchaud fractional derivatives; 4.4.2 Stirling functions S(α, k), α < 0, and their representations by Liouville fractional integrals; 4.4.3 Stirling functions S(a, k), a C, and their representations; 4.4.4 Stirling functions S(a, k), a C, and recurrence relations 4.4.5 Further properties and first applications of Stirling functions S(a, k), a C |
| Record Nr. | UNINA-9910451608703321 |
Baleanu D (Dumitru)
|
||
| Singapore, : World Scientific Pub. Co., 2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Fractional calculus [[electronic resource] ] : models and numerical methods / / Dumitru Baleanu ... [et al.]
| Fractional calculus [[electronic resource] ] : models and numerical methods / / Dumitru Baleanu ... [et al.] |
| Autore | Baleanu D (Dumitru) |
| Pubbl/distr/stampa | Singapore, : World Scientific Pub. Co., 2012 |
| Descrizione fisica | 1 online resource (426 p.) |
| Disciplina | 515.83 |
| Altri autori (Persone) | BaleanuD (Dumitru) |
| Collana | Series on complexity, nonlinearity and chaos |
| Soggetto topico |
Fractional calculus
Mathematical models |
| ISBN |
1-280-66952-7
9786613646453 981-4355-21-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Contents; Preface; 1. Preliminaries; 1.1 Fourier and Laplace Transforms; 1.2 Special Functions and Their Properties; 1.2.1 The Gamma function and related special functions; 1.2.2 Hypergeometric functions; 1.2.3 Mittag-Leffler functions; 1.3 Fractional Operators; 1.3.1 Riemann-Liouville fractional integrals and fractional derivatives; 1.3.2 Caputo fractional derivatives; 1.3.3 Liouville fractional integrals and fractional derivatives. Marchaud derivatives; 1.3.4 Generalized exponential functions; 1.3.5 Hadamard type fractional integrals and fractional derivatives
1.3.6 Fractional integrals and fractional derivatives of a function with respect to another function1.3.7 Grunwald-Letnikov fractional derivatives; 2. A Survey of Numerical Methods for the Solution of Ordinary and Partial Fractional Differential Equations; 2.1 Approximation of Fractional Operators; 2.1.1 Methods based on quadrature theory; 2.1.2 Grunwald-Letnikov methods; 2.1.3 Lubich's fractional linear multistep methods; 2.2 Direct Methods for Fractional ODEs; 2.2.1 The basic idea; 2.2.2 Quadrature-based direct methods; 2.3 Indirect Methods for Fractional ODEs; 2.3.1 The basic idea 2.3.2 An Adams-type predictor-corrector method2.3.3 The Cao-Burrage-Abdullah approach; 2.4 Linear Multistep Methods; 2.5 Other Methods; 2.6 Methods for Terminal Value Problems; 2.7 Methods for Multi-Term FDE and Multi-Order FDS; 2.8 Extension to Fractional PDEs; 2.8.1 General formulation of the problem; 2.8.2 Examples; 3. Efficient Numerical Methods; 3.1 Methods for Ordinary Differential Equations; 3.1.1 Dealing with non-locality; 3.1.2 Parallelization of algorithms; 3.1.3 When and when not to use fractional linear multistep formulas; 3.1.4 The use of series expansions 3.1.5 Adams methods for multi-order equations3.1.6 Two classes of singular equations as application examples; 3.2 Methods for Partial Differential Equations; 3.2.1 The method of lines; 3.2.2 BDFs for time-fractional equations; 3.2.3 Other methods; 3.2.4 Methods for equations with space-fractional operators; 4. Generalized Stirling Numbers and Applications; 4.1 Introduction; 4.2 Stirling Functions s(a, k), a C; 4.2.1 Equivalent definitions; 4.2.2 Multiple sum representations. The Riemann Zeta function; 4.3 General Stirling Functions s(α, β) with Complex Arguments 4.3.1 Definition and main result4.3.2 Differentiability of the s(α, β); The zeta function encore; 4.3.3 Recurrence relations for s(α, β); 4.4 Stirling Functions of the Second Kind S(α, k); 4.4.1 Stirling functions S(a, k), a 0, and their representations by Liouville and Marchaud fractional derivatives; 4.4.2 Stirling functions S(α, k), α < 0, and their representations by Liouville fractional integrals; 4.4.3 Stirling functions S(a, k), a C, and their representations; 4.4.4 Stirling functions S(a, k), a C, and recurrence relations 4.4.5 Further properties and first applications of Stirling functions S(a, k), a C |
| Record Nr. | UNINA-9910779010803321 |
|
Baleanu D (Dumitru)
|
||
| Singapore, : World Scientific Pub. Co., 2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Fractional calculus [[electronic resource] ] : models and numerical methods / / Dumitru Baleanu ... [et al.]
| Fractional calculus [[electronic resource] ] : models and numerical methods / / Dumitru Baleanu ... [et al.] |
| Autore | Baleanu D (Dumitru) |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Singapore, : World Scientific Pub. Co., 2012 |
| Descrizione fisica | 1 online resource (426 p.) |
| Disciplina | 515.83 |
| Altri autori (Persone) | BaleanuD (Dumitru) |
| Collana | Series on complexity, nonlinearity and chaos |
| Soggetto topico |
Fractional calculus
Mathematical models |
| ISBN |
1-280-66952-7
9786613646453 981-4355-21-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Contents; Preface; 1. Preliminaries; 1.1 Fourier and Laplace Transforms; 1.2 Special Functions and Their Properties; 1.2.1 The Gamma function and related special functions; 1.2.2 Hypergeometric functions; 1.2.3 Mittag-Leffler functions; 1.3 Fractional Operators; 1.3.1 Riemann-Liouville fractional integrals and fractional derivatives; 1.3.2 Caputo fractional derivatives; 1.3.3 Liouville fractional integrals and fractional derivatives. Marchaud derivatives; 1.3.4 Generalized exponential functions; 1.3.5 Hadamard type fractional integrals and fractional derivatives
1.3.6 Fractional integrals and fractional derivatives of a function with respect to another function1.3.7 Grunwald-Letnikov fractional derivatives; 2. A Survey of Numerical Methods for the Solution of Ordinary and Partial Fractional Differential Equations; 2.1 Approximation of Fractional Operators; 2.1.1 Methods based on quadrature theory; 2.1.2 Grunwald-Letnikov methods; 2.1.3 Lubich's fractional linear multistep methods; 2.2 Direct Methods for Fractional ODEs; 2.2.1 The basic idea; 2.2.2 Quadrature-based direct methods; 2.3 Indirect Methods for Fractional ODEs; 2.3.1 The basic idea 2.3.2 An Adams-type predictor-corrector method2.3.3 The Cao-Burrage-Abdullah approach; 2.4 Linear Multistep Methods; 2.5 Other Methods; 2.6 Methods for Terminal Value Problems; 2.7 Methods for Multi-Term FDE and Multi-Order FDS; 2.8 Extension to Fractional PDEs; 2.8.1 General formulation of the problem; 2.8.2 Examples; 3. Efficient Numerical Methods; 3.1 Methods for Ordinary Differential Equations; 3.1.1 Dealing with non-locality; 3.1.2 Parallelization of algorithms; 3.1.3 When and when not to use fractional linear multistep formulas; 3.1.4 The use of series expansions 3.1.5 Adams methods for multi-order equations3.1.6 Two classes of singular equations as application examples; 3.2 Methods for Partial Differential Equations; 3.2.1 The method of lines; 3.2.2 BDFs for time-fractional equations; 3.2.3 Other methods; 3.2.4 Methods for equations with space-fractional operators; 4. Generalized Stirling Numbers and Applications; 4.1 Introduction; 4.2 Stirling Functions s(a, k), a C; 4.2.1 Equivalent definitions; 4.2.2 Multiple sum representations. The Riemann Zeta function; 4.3 General Stirling Functions s(α, β) with Complex Arguments 4.3.1 Definition and main result4.3.2 Differentiability of the s(α, β); The zeta function encore; 4.3.3 Recurrence relations for s(α, β); 4.4 Stirling Functions of the Second Kind S(α, k); 4.4.1 Stirling functions S(a, k), a 0, and their representations by Liouville and Marchaud fractional derivatives; 4.4.2 Stirling functions S(α, k), α < 0, and their representations by Liouville fractional integrals; 4.4.3 Stirling functions S(a, k), a C, and their representations; 4.4.4 Stirling functions S(a, k), a C, and recurrence relations 4.4.5 Further properties and first applications of Stirling functions S(a, k), a C |
| Record Nr. | UNINA-9910816788503321 |
|
Baleanu D (Dumitru)
|
||
| Singapore, : World Scientific Pub. Co., 2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||