Fractal and Fractional (Apr 2024)

New Study on the Controllability of Non-Instantaneous Impulsive Hilfer Fractional Neutral Stochastic Evolution Equations with Non-Dense Domain

  • Gunasekaran Gokul,
  • Barakah Almarri,
  • Sivajiganesan Sivasankar,
  • Subramanian Velmurugan,
  • Ramalingam Udhayakumar

DOI
https://doi.org/10.3390/fractalfract8050265
Journal volume & issue
Vol. 8, no. 5
p. 265

Abstract

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The purpose of this work is to investigate the controllability of non-instantaneous impulsive (NII) Hilfer fractional (HF) neutral stochastic evolution equations with a non-dense domain. We construct a new set of adequate assumptions for the existence of mild solutions using fractional calculus, semigroup theory, stochastic analysis, and the fixed point theorem. Then, the discussion is driven by some suitable assumptions, including the Hille–Yosida condition without the compactness of the semigroup of the linear part. Finally, we provide examples to illustrate our main result.

Keywords