Nonlocal problems for a fractional order mixed parabolic equation

In the present work nonlocal problems with Bitsadze-Samarskii type conditions, with the first and the second kind integral conditions for mixed parabolic equation involving Riemann-Liouville fractional differential operator have been formulated and investigated. The uniqueness and the existence of the solution of the considered problems were proved. To do this, considered problems are equivalently reduced to the problems with nonlocal conditions with respect to the trace of the unknown function and its space-derivatives. Then using the representation of the solution of the second kind of Abel's integral equation, it was found integral representations of the solutions of these problems. Necessary conditions for the given functions were determined in order to provide a unique solvability of investigated problems.

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