Approximate Controllability of Abstract Discrete Fractional Systems of Order $$1

Rodrigo Ponce ()
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Rodrigo Ponce: Universidad de Talca

Journal of Optimization Theory and Applications, 2024, vol. 203, issue 1, No 15, 359-385

Abstract: Abstract We study the approximate controllability of the discrete fractional systems of order $$1 0$$ τ > 0 is a given step size. To do this, we first study resolvent sequences $$\{S_{\alpha ,\beta }^n\}_{n\in {\mathbb {N}}_0}$$ { S α , β n } n ∈ N 0 generated by closed linear operators to obtain some subordination results. In addition, we discuss the existence of solutions to $$(*)$$ ( ∗ ) and next, we study the existence of optimal controls to obtain the approximate controllability of the discrete fractional system $$(*)$$ ( ∗ ) in terms of the resolvent sequence $$\{S_{\alpha ,\beta }^n\}_{n\in {\mathbb {N}}_0}$$ { S α , β n } n ∈ N 0 for some $$\alpha ,\beta >0.$$ α , β > 0 . Finally, we provide an example to illustrate our results.

Keywords: Fractional discrete systems; Unbounded linear operators; Cosine families; Approximate controllability; 93C55; 39A12; 49M25; 26A33; 47D06 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10957-024-02516-0

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