Geodesic
Linear and quasilinear equations with several Gerasimov~--- Caputo derivatives
Čelâbinskij fiziko-matematičeskij žurnal, Tome 9 (2024) no. 1, pp. 5-22

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A representation of a solution of the Cauchy problem for a linear inhomogeneous equation solved with respect to the oldest derivative with several fractional Gerasimov — Caputo derivatives and with a sectorial pencil of linear closed operators at them in the case of the Hölder function in the right-hand side of the equation is obtained; the uniqueness of the solution is proved. This result is used to reduce the Cauchy problem for the corresponding quasilinear equation to an integro-differential equation. The existence of a unique local solution is proved by the method of contraction operators in the case of local Lipschitz nonlinear operator depending on several Gerasimov — Caputo derivatives in the equation and a single global solution under the Lipschitz condition for this operator.
Keywords: Gerasimov — Caputo fractional derivative, multi-term fractional equation, sectorial pencil of operators, Hölder function. 
@article{CHFMJ_2024_9_1_a0,
     author = {K. V. Boyko},
     title = {Linear and quasilinear equations with several {Gerasimov~---} {Caputo} derivatives},
     journal = {\v{C}el\^abinskij fiziko-matemati\v{c}eskij \v{z}urnal},
     pages = {5--22},
     publisher = {mathdoc},
     volume = {9},
     number = {1},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHFMJ_2024_9_1_a0/}
}
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K. V. Boyko. Linear and quasilinear equations with several Gerasimov~--- Caputo derivatives. Čelâbinskij fiziko-matematičeskij žurnal, Tome 9 (2024) no. 1, pp. 5-22. http://geodesic.mathdoc.fr/item/CHFMJ_2024_9_1_a0/