Generators of Analytic Resolving Families for Distributed Order Equations and Perturbations

Vladimir E. Fedorov
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Vladimir E. Fedorov: Department of Mathematical Analysis, Chelyabinsk State University, 454001 Chelyabinsk, Russia

Mathematics, 2020, vol. 8, issue 8, 1-15

Abstract: Linear differential equations of a distributed order with an unbounded operator in a Banach space are studied in this paper. A theorem on the generation of analytic resolving families of operators for such equations is proved. It makes it possible to study the unique solvability of inhomogeneous equations. A perturbation theorem for the obtained class of generators is proved. The results of the work are illustrated by an example of an initial boundary value problem for the ultraslow diffusion equation with the lower-order terms with respect to the spatial variable.

Keywords: distributed order equation; analytic resolving family of operators; generator of resolving family; perturbation theorem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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