Some Nonlocal Boundary-Value Problems for the Biparabolic Evolution Equation and Its Fractional-Differential Analog

Abstract

For the biparabolic partial differential evolution equation and its fractional differential generalization, statements are made and closed-form solutions of some boundary-value problems with nonlocal boundary conditions are obtained. Variants of direct and inverse problem statements are considered. The mathematical formulation of the inverse problem involves the search, together with the solution of the original integro-differential equation of fractional order, of its unknown right-hand side as well, which functionally depends only on the geometric variable.