Bulavatsky V.M.
Some nonlocal boundary-value problems for biparabolic evolution equation and its fractional differential analogue

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. © 2019, Springer Science+Business Media, LLC, part of Springer Nature.

Keywords: biorthogonal systems of functions, biparabolic evolution equation, fractional-differential analog of biparabolic equation, inverse problem, nonlocal boundary-value problem, Boundary conditions, Boundary value problems, Evolutionary algorithms, Fourier analysis, Integrodifferential equations, Optimization, Biorthogonal, Differential equation of fractional order, Direct and inverse problems, Evolution equations, Fractional differential, Mathematical formulation, Non-local boundary conditions, Nonlocal boundary-value problems, Inverse problems

Cite:
Bulavatsky V.M. (2019). Some nonlocal boundary-value problems for biparabolic evolution equation and its fractional differential analogue. Cybernetics and Systems Analysis, 55 (5), 106-114. doi: https://doi.org/10.1007/s10559-019-00190-z http://jnas.nbuv.gov.ua/article/UJRN-0001018668 [In Russian].