Solvability of the boundary-value problem for a linear loaded integro-differential equation in an infinite three-dimensional domain

In this work we study a boundary-value problem for a loaded mixed type equation in an infinite three-dimensional domain. Purpose of this work is to solve biological population model of the generalized fractional order differential equation involving the Riemann-Liouville operators. We will study constructing optimal representations of the solution in each domain and under certain additional conditions to study questions of the existence and uniqueness of solution of boundary-value problems.