Degenerate Multi-Term Equations with Gerasimov–Caputo Derivatives in the Sectorial Case

Vladimir E. Fedorov () and Kseniya V. Boyko
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Vladimir E. Fedorov: Department of Mathematical Analysis, Mathematics Faculty, Chelyabinsk State University, Kashirin Brothers St. 129, 454001 Chelyabinsk, Russia
Kseniya V. Boyko: Department of Mathematical Analysis, Mathematics Faculty, Chelyabinsk State University, Kashirin Brothers St. 129, 454001 Chelyabinsk, Russia

Mathematics, 2022, vol. 10, issue 24, 1-12

Abstract: The unique solvability for the Cauchy problem in a class of degenerate multi-term linear equations with Gerasimov–Caputo derivatives in a Banach space is investigated. To this aim, we use the condition of sectoriality for the pair of operators at the oldest derivatives from the equation and the general conditions of the other operators’ coordination with invariant subspaces, which exist due to the sectoriality. An abstract result is applied to the research of unique solvability issues for the systems of the dynamics and of the thermoconvection for some viscoelastic media.

Keywords: Gerasimov–Caputo derivative; fractional differential equation; analytic resolving family of operators; degenerate evolution equation; multi-term fractional equation; initial value problem; initial boundary value problem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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