Fundamental solutions for semidiscrete evolution equations via Banach algebras

We give representations for solutions of time-fractional differential equations that involve operators on Lebesgue spaces of sequences defined by discrete convolutions involving kernels through the discrete Fourier transform. We consider finite difference operators of first and second orders, which...

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Bibliographic Details
Published in:Advances in difference equations 2021-01, Vol.2021 (1), p.35-35, Article 35
Main Authors: González-Camus, Jorge, Lizama, Carlos, Miana, Pedro J.
Format: Article
Language:English
Subjects:
Analysis
Caputo fractional derivative
Continuity (mathematics)
Difference and Functional Equations
Differential equations
Discrete fractional Laplacian
Discrete fractional operators
Finite difference method
Finite differences
Fourier transforms
Functional Analysis
Fundamental solutions
Generators
Mathematical analysis
Mathematics
Mathematics and Statistics
Norms
Operators (mathematics)
Ordinary Differential Equations
Partial Differential Equations
Trigonometric functions
Wright and Mittag-Leffler functions
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Summary:We give representations for solutions of time-fractional differential equations that involve operators on Lebesgue spaces of sequences defined by discrete convolutions involving kernels through the discrete Fourier transform. We consider finite difference operators of first and second orders, which are generators of uniformly continuous semigroups and cosine functions. We present the linear and algebraic structures (in particular, factorization properties) and their norms and spectra in the Lebesgue space of summable sequences. We identify fractional powers of these generators and apply to them the subordination principle. We also give some applications and consequences of our results.
ISSN:1687-1839
1687-1847
1687-1847
DOI:10.1186/s13662-020-03206-7