On Solvability of Some Inverse Problems for a Fractional Parabolic Equation with a Nonlocal Biharmonic Operator

Abstract

The paper considers the solvability of some inverse problems for fractional differential equations with a nonlocal biharmonic operator, which is introduced with the help of involutive transformations in two space variables. The considered problems are solved using the Fourier method. The properties of eigenfunctions and associated functions of the corresponding spectral problems are studied. Theorems on the existence and uniqueness of solutions to the studied problems are proved.

Keywords

• inverse problem
• fractional derivative
• involution
• nonlocal operator
• parabolic equation
• fourth order equation