| Citation: |
Shouguo Zhu. $L^{p}$-NULL CONTROLLABILITY OF A $\psi$-CAPUTO FRACTIONAL EVOLUTION SYSTEM[J]. Journal of Applied Analysis & Computation, 2026, 16(5): 2238-2263. doi: 10.11948/20250251
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$L^{p}$-NULL CONTROLLABILITY OF A $\psi$-CAPUTO FRACTIONAL EVOLUTION SYSTEM
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Abstract
This article intends to investigate the $L^{p}$-null controllability of an abstract system involving the $\psi$-Caputo fractional derivative in a Banach space. By leveraging the operator $L_{0}^{-1}$ and integrating the improved approximation solvability technique with the resolvent approach, we first explore this problem without relying on the compactness of the semigroup, Lipschitz continuity of the perturbation item or noncompactness measure conditions. Subsequently, by introducing suitable conditions and combining Banach's fixed point theorem with the integral contractor method, we tackle this problem?independent of $L_{0}^{-1}$. Finally, we offer two concrete examples to confirm the practical applicability of our mentioned findings.
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References
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Shouguo Zhu. $L^{p}$-NULL CONTROLLABILITY OF A $\psi$-CAPUTO FRACTIONAL EVOLUTION SYSTEM[J]. Journal of Applied Analysis & Computation, 2026, 16(5): 2238-2263. doi: 10.11948/20250251
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