Finite-approximate controllability of riemann–liouville fractional evolution systems via resolvent-like operators

Mahmudov N.

Fractal and Fractional, vol.5, no.4, 2021 (SCI-Expanded) identifier

  • Nəşrin Növü: Article / Article
  • Cild: 5 Say: 4
  • Nəşr tarixi: 2021
  • Doi nömrəsi: 10.3390/fractalfract5040199
  • jurnalın adı: Fractal and Fractional
  • Jurnalın baxıldığı indekslər: Science Citation Index Expanded (SCI-EXPANDED), Scopus, INSPEC, Directory of Open Access Journals
  • Açar sözlər: Evolution equation, Finite-approximate controllability, Riemann–liouville fractional systems
  • Açıq Arxiv Kolleksiyası: Məqalə
  • Adres: Yox

Qısa məlumat

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.