Analytic in a Sector Resolving Families of Operators for Degenerate Evolution Fractional Equations

Journal Article · Mon Jan 15 00:00:00 EST 2018 · Journal of Mathematical Sciences

DOI:https://doi.org/10.1007/S10958-017-3629-4· OSTI ID:22771605

Fedorov, V. E., E-mail: [e-mail]; Romanova, E. A., E-mail: [e-mail] ^[1]; Debbouche, A., E-mail: [e-mail] ^[2]

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1. Chelyabinsk State University (Russian Federation)
2. Université 8 Mai 1945 (Algeria)

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.

• OSTI ID: 22771605
• Journal Information: Journal of Mathematical Sciences, Vol. 228, Issue 4; Other Information: Copyright (c) 2018 Springer Science+Business Media, LLC, part of Springer Nature; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); ISSN 1072-3374
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
BANACH SPACE
BOUNDARY-VALUE PROBLEMS
KERNELS
LAPLACIAN
MATHEMATICAL EVOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
PHASE SPACE
POLYNOMIALS