Geodesic
Quasilinear equations with fractional Gerasimov--Caputo derivative. Sectorial case
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Mathematical Physics, Tome 226 (2023), pp. 127-137

Voir la notice de l'article provenant de la source Math-Net.Ru

We study initial-value problems for quasilinear equations with Gerasimov–Caputo fractional derivatives in Banach spaces whose linear part has an analytic resolving family of operators in the sector. The nonlinear operator is assumed to be a locally Lipschitz operator. We consider equations that are solved with respect to the highest derivative and equations containing a degenerate linear operator acting on the highest derivative. The theorem on the unique solvability of the Cauchy problem proved in the paper is used for the study of the unique solvability of the Showalter–Sidorov problem for degenerate equations. Abstract results are applied to the initial-boundary-value problem for partial differential equations that are not solvable with respect to the highest fractional derivative in time.
Keywords: quasilinear equation, Gerasimov–Caputo fractional derivative, sectorial operator, Cauchy problem, initial boundary value problem. 
@article{INTO_2023_226_a12,
     author = {V. E. Fedorov and T. A. Zaharova},
     title = {Quasilinear equations with fractional {Gerasimov--Caputo} derivative. {Sectorial} case},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {127--137},
     publisher = {mathdoc},
     volume = {226},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2023_226_a12/}
}
TY  - JOUR
AU  - V. E. Fedorov
AU  - T. A. Zaharova
TI  - Quasilinear equations with fractional Gerasimov--Caputo derivative. Sectorial case
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2023
SP  - 127
EP  - 137
VL  - 226
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2023_226_a12/
LA  - ru
ID  - INTO_2023_226_a12
ER  - 
%0 Journal Article
%A V. E. Fedorov
%A T. A. Zaharova
%T Quasilinear equations with fractional Gerasimov--Caputo derivative. Sectorial case
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2023
%P 127-137
%V 226
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2023_226_a12/
%G ru
%F INTO_2023_226_a12
V. E. Fedorov; T. A. Zaharova. Quasilinear equations with fractional Gerasimov--Caputo derivative. Sectorial case. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Mathematical Physics, Tome 226 (2023), pp. 127-137. http://geodesic.mathdoc.fr/item/INTO_2023_226_a12/