UDC 517.9 : 519.6
1 V.M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine
 v_bulav@ukr.net
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SOME NONLOCAL BOUNDARY-VALUE PROBLEMS FOR BIPARABOLIC
EVOLUTION EQUATION AND ITS FRACTIONAL DIFFERENTIAL ANALOGUEE
Abstract. For biparabolic evolution partial differential 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 also its unknown right-hand side that depends functionally only on the geometric variable
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Keywords: biparabolic evolution equation, fractional-differential analogue of biparabolic equation, nonlocal boundary value problem, inverse problem, biorthogonal systems of functions.
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