Abstract
The Cauchy problem for linear multi-term equations in Banach spaces with the fractional Gerasimov–Caputo derivatives and with linear closed operators at them is studied. It was proved that the homogeneous equation has an analytic in a sector resolving family of operators, if and only if the tuple of operators from the equation belongs to the class \(\mathcal{A}^{n,r}_{\alpha,G}(\theta_{0},a_{0})\), which is introduced here. Theorem on the existence and uniqueness of a solution to the inhomogeneous Cauchy problem is proved. Abstract results are applied in the study of initial-boundary value problems for equations with Gerasimov–Caputo derivatives in time and with polynomials of a self-adjoint elliptic differential operator with respect to spatial variables.
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The work is funded by the Russian Foundation for Basic Research and the Vietnam Academy of Science and Technology, grant no. 21-51-54003.
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(Submitted by A. B. Muravnik)
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Boyko, K.V., Fedorov, V.E. The Cauchy Problem for a Class of Multi-Term Equations with Gerasimov–Caputo Derivatives. Lobachevskii J Math 43, 1293–1302 (2022). https://doi.org/10.1134/S1995080222090049
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DOI: https://doi.org/10.1134/S1995080222090049