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Fractional Laplace operator and its properties
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Mateusz Kwaśnicki
Abstract
The fractional Laplace operator appears in various areas of pure and applied mathematics. This survey collects several equivalent definitions of this operator, most known explicit expressions, a sample of regularity results and a number of restrictions of this operator to a domain. Connections to isotropic stable Lévy processes are also discussed.
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Abstract
The fractional Laplace operator appears in various areas of pure and applied mathematics. This survey collects several equivalent definitions of this operator, most known explicit expressions, a sample of regularity results and a number of restrictions of this operator to a domain. Connections to isotropic stable Lévy processes are also discussed.
You are currently not able to access this content.
Chapters in this book
- Frontmatter I
- Preface V
- Contents VII
- Recent history of the fractional calculus: data and statistics 1
- Basic FC operators and their properties 23
- Mathematical and physical interpretations of fractional derivatives and integrals 47
- Generalized fractional calculus operators with special functions 87
- General fractional calculus 111
- Multiple Erdélyi–Kober integrals and derivatives as operators of generalized fractional calculus 127
- Fractional Laplace operator and its properties 159
- Applications of the Mellin integral transform technique in fractional calculus 195
- Fractional Fourier transform 225
- The Wright function and its applications 241
- Mittag-Leffler function: properties and applications 269
- Asymptotics of the special functions of fractional calculus 297
- Analysis of fractional integro-differential equations of thermistor type 327
- A survey on fractional variational calculus 347
- Variational principles with fractional derivatives 361
- Continuous time random walks and space-time fractional differential equations 385
- Inverse subordinators and time fractional equations 407
- Spectral theory of fractional order integration operators, their direct sums, and similarity problem to these operators of their weak perturbations 427
- Fractional differentiation in p-adic analysis 461
- Index 473
Chapters in this book
- Frontmatter I
- Preface V
- Contents VII
- Recent history of the fractional calculus: data and statistics 1
- Basic FC operators and their properties 23
- Mathematical and physical interpretations of fractional derivatives and integrals 47
- Generalized fractional calculus operators with special functions 87
- General fractional calculus 111
- Multiple Erdélyi–Kober integrals and derivatives as operators of generalized fractional calculus 127
- Fractional Laplace operator and its properties 159
- Applications of the Mellin integral transform technique in fractional calculus 195
- Fractional Fourier transform 225
- The Wright function and its applications 241
- Mittag-Leffler function: properties and applications 269
- Asymptotics of the special functions of fractional calculus 297
- Analysis of fractional integro-differential equations of thermistor type 327
- A survey on fractional variational calculus 347
- Variational principles with fractional derivatives 361
- Continuous time random walks and space-time fractional differential equations 385
- Inverse subordinators and time fractional equations 407
- Spectral theory of fractional order integration operators, their direct sums, and similarity problem to these operators of their weak perturbations 427
- Fractional differentiation in p-adic analysis 461
- Index 473
