On a boundary value problem in a half-strip for a fourth-order parabolic equation with a Riemann-Liouville operator in a time variable

In this work a fourth-order inhomogeneous parabolic equation with time fractional derivative is considered. The boundary-value problem in the half-strip for equation under consideration is studied. In this paper a fundamental solution for fourth-order parabolic equation with time fractional derivative in terms of the Wright function is presented, а representation of the solution of the problem is constructed and uniqueness of the solution in the class of fast growth functions is proved.