Linear equations with discretely distributed fractional derivative in Banach spaces
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 27 (2021) no. 2, pp. 264-280
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We study the unique solvability of linear equations in Banach spaces with discretely distributed Gerasimov–Caputo fractional derivative in terms of analytic resolving families of operators. Necessary and sufficient conditions for the existence of such a family of operators are obtained in terms of the resolvent of a closed operator from the right-hand side of the equation, and the properties of this family are studied. These results are used to prove the existence of a unique solution to the Cauchy problem for a linear equation of the corresponding class with inhomogeneity which is either continuous in the norm of the graph of the operator from the right-hand side of the equation or Hölderian. Based on the abstract results obtained, we investigate the unique solvability of initial–boundary value problems for a class of equations with discretely distributed fractional time derivative and with polynomials in an elliptic self-adjoint differential operator with respect to spatial variables.
Keywords:
Gerasimov–Caputo fractional derivative, discretely distributed fractional derivative, Cauchy problem, resolving family of operators, initial–boundary value problem.
@article{TIMM_2021_27_2_a21,
author = {V. E. Fedorov and N. V. Filin},
title = {Linear equations with discretely distributed fractional derivative in {Banach} spaces},
journal = {Trudy Instituta matematiki i mehaniki},
pages = {264--280},
publisher = {mathdoc},
volume = {27},
number = {2},
year = {2021},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TIMM_2021_27_2_a21/}
}
TY - JOUR AU - V. E. Fedorov AU - N. V. Filin TI - Linear equations with discretely distributed fractional derivative in Banach spaces JO - Trudy Instituta matematiki i mehaniki PY - 2021 SP - 264 EP - 280 VL - 27 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TIMM_2021_27_2_a21/ LA - ru ID - TIMM_2021_27_2_a21 ER -
%0 Journal Article %A V. E. Fedorov %A N. V. Filin %T Linear equations with discretely distributed fractional derivative in Banach spaces %J Trudy Instituta matematiki i mehaniki %D 2021 %P 264-280 %V 27 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/TIMM_2021_27_2_a21/ %G ru %F TIMM_2021_27_2_a21
V. E. Fedorov; N. V. Filin. Linear equations with discretely distributed fractional derivative in Banach spaces. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 27 (2021) no. 2, pp. 264-280. http://geodesic.mathdoc.fr/item/TIMM_2021_27_2_a21/