Abstract
We show that fractional powers of general sectorial operators on Banach spaces can be obtained by the harmonic extension approach. Moreover, for the corresponding second order ordinary differential equation with incomplete data describing the harmonic extension we prove existence and uniqueness of a bounded solution (i.e., of the harmonic extension).
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© 2020 Diogenes Co., Sofia
Articles in the same Issue
- Frontmatter
- Editorial Note
- FCAA related news, events and books (FCAA–VOLUME 23–4–2020)
- Editorial Survey
- Fractional derivatives and the fundamental theorem of fractional calculus
- Research Paper
- Erdélyi–Kober fractional integrals and radon transforms for mutually orthogonal affine planes
- Nontrivial solutions of non-autonomous dirichlet fractional discrete problems
- Applications of Hilfer-Prabhakar operator to option pricing financial model
- On a quantitative theory of limits: Estimating the speed of convergence
- Global solutions and blowing-up solutions for a nonautonomous and nonlocal in space reaction-diffusion system with Dirichlet boundary conditions
- On the harmonic extension approach to fractional powers in Banach spaces
- Initial-value / Nonlocal Cauchy problems for fractional differential equations involving ψ-Hilfer multivariable operators
- Fractional abstract Cauchy problem on complex interpolation scales
- On representation formulas for solutions of linear differential equations with Caputo fractional derivatives
- Asymptotics of fundamental solutions for time fractional equations with convolution kernels
- Attractivity for differential equations of fractional order and ψ-Hilfer type
- Semilinear fractional elliptic problems with mixed Dirichlet-Neumann boundary conditions
Articles in the same Issue
- Frontmatter
- Editorial Note
- FCAA related news, events and books (FCAA–VOLUME 23–4–2020)
- Editorial Survey
- Fractional derivatives and the fundamental theorem of fractional calculus
- Research Paper
- Erdélyi–Kober fractional integrals and radon transforms for mutually orthogonal affine planes
- Nontrivial solutions of non-autonomous dirichlet fractional discrete problems
- Applications of Hilfer-Prabhakar operator to option pricing financial model
- On a quantitative theory of limits: Estimating the speed of convergence
- Global solutions and blowing-up solutions for a nonautonomous and nonlocal in space reaction-diffusion system with Dirichlet boundary conditions
- On the harmonic extension approach to fractional powers in Banach spaces
- Initial-value / Nonlocal Cauchy problems for fractional differential equations involving ψ-Hilfer multivariable operators
- Fractional abstract Cauchy problem on complex interpolation scales
- On representation formulas for solutions of linear differential equations with Caputo fractional derivatives
- Asymptotics of fundamental solutions for time fractional equations with convolution kernels
- Attractivity for differential equations of fractional order and ψ-Hilfer type
- Semilinear fractional elliptic problems with mixed Dirichlet-Neumann boundary conditions