Information on the thesis

New sucient conditions of the classical solvability and maximum
regularity of solutions of the nonlinear Hammerstein type operator-
dierential equations with kernels on complex interpolation scales of sectorial
operators, an abstract fractional Cauchy problem, also under linear and nonli-
near perturbations, are found. The obtained results are dened concretele to
the operators generated by regular elliptic boundary value problems.
Using the analytic properties of the sectorial operators’ functional
calculus, a new method of approximation of a solution of an abstract
fractional Cauchy problem, perturbed on complex interpolation scales of a
sectorial operator, built without restrictions on the norm of the perturbed
operator, the approximations of solutions of normal parabolic boundary value
problems, perturbed by pseudodierential terms, built with the use of iterati-
ons of the Green operators of nutbourne boundary value problems.
Unique solvability of direct and some inverse time-space fractional
Cauchy problems and boundary value problems for a time fractional diusion-
wave equations in spaces of distributions and smooth, in particular, with
values in Bessel potentials spaces, are obtained.
Key words: distribution, fractional derivative, complex interpolation
scales, Bessel potentials spaces, nonlinear integral-dierential equations,
maximum regularity of solution, regular elliptic dierential operator, sectorial
operator, functional calculus, Wiener type algebras.