Geodesic
Continuous dependence on parameters of differential inclusion using new techniques of fixed point theory
Filomat, Tome 37 (2023) no. 16, p. 5469

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DOI

In this paper, we establish the global existence and the continuous dependence on parameters for a set solutions to a class of time-fractional partial differential equation in the form ∂ ∂t u(t) +KAσ1 ∂ ∂t u(t) +Aσ2 u(t) ∈ F(t,u(t), µ), t ∈ I, u(T) = h, ( resp. u(0) = h) on Ω, where σ1, σ2 > 0 andI = [0,T) (resp. I = (0,T]). Precisely, first results are about the global existence of mild solutions and the compactness of the mild solutions set. These result are mainly based on some necessary estimates derived by considering the solution representation in Hilbert spaces. The remaining result is the continuous dependence of the solutions set on some special parameters. The main technique used in this study include the fixed point theory and some certain conditions of multivalued operators.
DOI : 10.2298/FIL2316469T
Classification : 35R11, 35B65, 26A33
Keywords: Multi-function, Measure of compactness, Differential inclusion, Self-Adjoint operator 
Vo Viet Tria. Continuous dependence on parameters of differential inclusion using new techniques of fixed point theory. Filomat, Tome 37 (2023) no. 16, p. 5469 . doi: 10.2298/FIL2316469T
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     author = {Vo Viet Tria},
     title = {Continuous dependence on parameters of differential inclusion using new techniques of fixed point theory},
     journal = {Filomat},
     pages = {5469 },
     year = {2023},
     volume = {37},
     number = {16},
     doi = {10.2298/FIL2316469T},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2316469T/}
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