Electronic Journal of Differential Equations, Vol. 2022 (2022), No. 56, pp. 1-20.

Title: A parabolic bipolynomial fractional Dirichlet-Laplace problem
       
Author: Dariusz Idczak (Univ. of Lodz, Lodz, Poland)

Abstract:  
We derive existence results for a parabolic bipolynomial abstract and
classical problems containing fractional powers of the Dirichlet-Laplace operator
on a bounded domain,  in the sense of the Stone-von Neumann operator calculus.
The main tools are theorems on the existence and uniqueness of a weak
solutions to an abstract problem, due to Friedman, and a general theorem on
the equivalence of weak and strong solutions to some operator equation.

Submitted December 8, 2021. Published July 31, 2022.
Math Subject Classifications: 35K10, 35R11.
Key Words: Parabolic equation; fractional Dirichlet-Laplace operator;
           existence of solutions.