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A Cauchy Type Problem for a Degenerate Equation with the Riemann–Liouville Derivative in the Sectorial Case

Siberian Mathematical Journal, ISSN: 0037-4466, Vol: 60, Issue: 2, Page: 359-372
2019
  • 23
    Citations
  • 0
    Usage
  • 4
    Captures
  • 0
    Mentions
  • 0
    Social Media
Metric Options:   Counts1 Year3 Year

Metrics Details

  • Citations
    23
    • Citation Indexes
      23
  • Captures
    4

Article Description

Under study is the unique solvability of a Cauchy type problem and a generalized Schowalter–Sidorov type problem for a class of linear inhomogeneous equations in Banach spaces with a degenerate operator at the Riemann–Liouville fractional derivative. We find an explicit form of a solution under some conditions for the pair of operators in the equation. To this end, we study a Cauchy type problem for an equation solvable with respect to the Riemann–Liouville derivative with an operator on the right-hand side which generates a resolving family of operators analytic in a sector. These abstract results are used to prove the unique solvability of an initial-boundary value problem for the Navier–Stokes system of equations of fractional order in time.

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