Abstract
An fractional abstract Cauchy problem generated by a sectorial operator is investigated. An inequality of coercivity type for its solution with respect to a complex interpolation scale generated by a sectorial operator with the same parameters is established. An application to differential parabolic initial-boundary value problems in bounded domains with a fractional time derivative is shown.
Acknowledgements
The authors would like to thank referees for their valuable comments, which helped to correct inaccuracies and improve the manuscript.
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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