Inverse initial-value problem in the spaces of Bessel potentials
DOI:
https://doi.org/10.3842/umzh.v77i11.9199Keywords:
fractional derivative, fractional diffusion equation, convolution, spaces of Bessel potentials, Green's vector-function, integral equationAbstract
UDC 517.95
We study the inverse problem of reconstruction (in the entire scale of spaces of Bessel potentials) of the initial values of the solution to a time-space fractional diffusion equation with a time-integral additional condition. We also establish sufficient conditions for the unique solvability of the inverse problem.
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