Degenerate Linear Evolution Equations with the Riemann–Liouville Fractional Derivative

Сибирский математический журнал

M. V. Plekhanova¹  V. E. Fedorov² 

[1] Chelyabinsk State University;Chelyabinsk State University South Ural State University

关键词: degenerate evolution equation;    Riemann–Liouville derivative;    Cauchy type problem;    Mittag-Leffler type operator function;    initial-boundary value problem;    Scott-Blair medium;   

DOI  :  10.1134/S0037446618010159

学科分类：数学（综合）

来源: Izdatel stvo Instituta Matematiki Rossiiskoi Akademii Nauk

【 摘 要 】

We study the unique solvability of the Cauchy and Schowalter–Sidorov type problems in a Banach space for an evolution equation with a degenerate operator at the fractional derivative under the assumption that the operator acting on the unknown function in the equation is p-bounded with respect to the operator at the fractional derivative. The conditions are found ensuring existence of a unique solution representable by means of the Mittag-Leffler type functions. Some abstract results are illustrated by an example of a finite-dimensional degenerate system of equations of a fractional order and employed in the study of unique solvability of an initial-boundary value problem for the linearized Scott-Blair system of dynamics of a medium.

【 授权许可】

CC BY