Finite-Approximate Controllability of Riemann–Liouville Fractional Evolution Systems via Resolvent-Like Operators

This paper presents a variational method for studying approximate controllability and infinite-dimensional exact controllability (finite-approximate controllability) for Riemann–Liouville fractional linear/semilinear evolution equations in Hilbert spaces. A useful criterion for finite-approximate co...

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Bibliographic Details
Published inFractal and fractional Vol. 5; no. 4; p. 199
Main Author Mahmudov, Nazim I.
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.12.2021
Subjects
Approximation
Banach spaces
Controllability
evolution equation
finite-approximate controllability
Hilbert space
Linear evolution equations
Mathematical analysis
Operators
Riemann–Liouville fractional systems
Stochastic control theory
Thermodynamics
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Summary:This paper presents a variational method for studying approximate controllability and infinite-dimensional exact controllability (finite-approximate controllability) for Riemann–Liouville fractional linear/semilinear evolution equations in Hilbert spaces. A useful criterion for finite-approximate controllability of Riemann–Liouville fractional linear evolution equations is formulated in terms of resolvent-like operators. We also find that such a control provides finite-dimensional exact controllability in addition to the approximate controllability requirement. Assuming the finite-approximate controllability of the corresponding linearized RL fractional evolution equation, we obtain sufficient conditions for finite-approximate controllability of the semilinear RL fractional evolution equation under natural conditions. The results are a generalization and continuation of recent results on this subject. Applications to fractional heat equations are considered.
ISSN:2504-3110
2504-3110
DOI:10.3390/fractalfract5040199