Determination of the Source Function by Additional Nonlinear Condition for a Fractional Hilfer Equation with a Square of the Pseudoparabolic Operator

In this paper, the questions of unique solvability of an inverse boundary value problem for an inhomogeneous differential equation containing a square of Hilfer fractional analogue of the Barenblatt–Zheltov–Kochina operator and two spatial variables are studied. The redefinition function is given in boundary condition and the additional condition has the nonlinear form. The Fourier series method based on the separation of variables is used. Sufficient coefficient conditions for unique classical solvability of the direct and inverse boundary value problems are established.