Analytic in a sector resolving families of operators for degenerate evolution fractional equations. (Russian, English) Zbl 1399.34012
Sib. Zh. Chist. Prikl. Mat. 16, No. 2, 93-107 (2016); translation in J. Math. Sci., New York 228, No. 4, 380-394 (2018).
Summary: We introduce a class of pairs of operators defining a linear homogeneous degenerate evolution fractional differential equation in a Banach space. Reflexive Banach spaces are represented as the direct sums of the phase space of the equation and the kernel of the operator at the fractional derivative. In a sector of the complex plane containing the positive half-axis, we construct an analytic family of resolving operators that degenerate only on the kernel. The results are used in the study of the solvability of initial-boundary value problems for partial differential equations containing fractional time-derivatives and polynomials in the Laplace operator with respect to the spatial variable.
MSC:
| 34A08 | Fractional ordinary differential equations |
| 35R11 | Fractional partial differential equations |
| 34G10 | Linear differential equations in abstract spaces |
| 34M99 | Ordinary differential equations in the complex domain |
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