Abstract
The present paper deals with fractional powers of positive operators in a Banach space. The main theorem concerns the structure of fractional powers of positive operators in fractional spaces. As applications, the structure of fractional powers of elliptic operators is studied.
Acknowledgements
This project was conducted with the support of the “RUDN University Program 5-100” and published under target program BR05236656 of the Science Committee of the Ministry of Education and Science of the Republic of Kazakhstan. Finally, some of statements of the present paper were formulated in [7] without proof. The authors are grateful to Prof. Virgina Kiryakova and referee of this paper for the useful comments and relevant references.
References
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© 2019 Diogenes Co., Sofia
Articles in the same Issue
- Frontmatter
- Editorial Note
- FCAA related news, events and books (FCAA–Volume 22–2–2019)
- Discussion Paper
- The flaw in the conformable calculus: It is conformable because it is not fractional
- The failure of certain fractional calculus operators in two physical models
- Research Paper
- Inverse problems for a class of degenerate evolution equations with Riemann – Liouville derivative
- On Riesz derivative
- A note on fractional powers of strongly positive operators and their applications
- Semi-fractional diffusion equations
- Extremum principle for the Hadamard derivatives and its application to nonlinear fractional partial differential equations
- Well-posedness of fractional degenerate differential equations in Banach spaces
- Structure factors for generalized grey Browinian motion
- Linear stationary fractional differential equations
- Perfect control for right-invertible Grünwald-Letnikov plants – an innovative approach to practical implementation
- On fractional differential inclusions with Nonlocal boundary conditions
- On solutions of linear fractional differential equations and systems thereof
- Existence of mild solution of a class of nonlocal fractional order differential equation with not instantaneous impulses
- A CAD-based algorithm for solving stable parameter region of fractional-order systems with structured perturbations
- On representation and interpretation of Fractional calculus and fractional order systems
Articles in the same Issue
- Frontmatter
- Editorial Note
- FCAA related news, events and books (FCAA–Volume 22–2–2019)
- Discussion Paper
- The flaw in the conformable calculus: It is conformable because it is not fractional
- The failure of certain fractional calculus operators in two physical models
- Research Paper
- Inverse problems for a class of degenerate evolution equations with Riemann – Liouville derivative
- On Riesz derivative
- A note on fractional powers of strongly positive operators and their applications
- Semi-fractional diffusion equations
- Extremum principle for the Hadamard derivatives and its application to nonlinear fractional partial differential equations
- Well-posedness of fractional degenerate differential equations in Banach spaces
- Structure factors for generalized grey Browinian motion
- Linear stationary fractional differential equations
- Perfect control for right-invertible Grünwald-Letnikov plants – an innovative approach to practical implementation
- On fractional differential inclusions with Nonlocal boundary conditions
- On solutions of linear fractional differential equations and systems thereof
- Existence of mild solution of a class of nonlocal fractional order differential equation with not instantaneous impulses
- A CAD-based algorithm for solving stable parameter region of fractional-order systems with structured perturbations
- On representation and interpretation of Fractional calculus and fractional order systems