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Controllability of fractional backward evolution equations with order α∈(1,2)

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  • Li, Qien
  • Luo, Danfeng

Abstract

This paper investigates the approximate and exact controllability of a class of fractional backward evolution equations with order 1<α<2 in Hilbert spaces. First, by employing the Tikhonov-type regularization method to construct an approximate control function, we establish sufficient conditions for the approximate controllability of the system via Schauder′s fixed point theorem. Subsequently, the exact controllability of the system is systematically studied under two distinct cases: the compact semigroup case and the noncompact semigroup case. In particular, for the noncompact case, the controllability results are derived by utilizing the Mönch′s fixed point theorem combined with the technique of measures of non-compactness. Finally, an example is provided to verify the validity of the proposed theoretical results.

Suggested Citation

  • Li, Qien & Luo, Danfeng, 2026. "Controllability of fractional backward evolution equations with order α∈(1,2)," Chaos, Solitons & Fractals, Elsevier, vol. 208(P2).
    • Handle: RePEc:eee:chsofr:v:208:y:2026:i:p2:s0960077926003541
    DOI: 10.1016/j.chaos.2026.118213
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