Geodesic
Existence and uniqueness theorem for a weak solution of fractional parabolic problem by the Rothe method
Nanosistemy: fizika, himiâ, matematika, Tome 15 (2024) no. 1, pp. 5-15.

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

This paper aims to study the existence and uniqueness of a weak solution for the boundary value problem of a time fractional equation involving the Caputo fractional derivative with an integral operator. By utilizing the discretization method, we first derive some a priori estimates for the approximate solutions at the points $(x, t_j)$. We then evaluate the accuracy of the proposed method to demonstrate that the implemented sequence of $\alpha$-Rothe functions converges in a certain sense, and its limit is the solution (in a weak sense) of our problem. It must be pointed out that the constructed L1 scheme is designed to approximate the Caputo fractional derivative mentioned in the problem.
Keywords: weak solution, a priori estimates, Rothe's method.
Mots-clés : Fractional diffusion equation 
@article{NANO_2024_15_1_a0,
     author = {Y. Bekakra and A. Bouziani},
     title = {Existence and uniqueness theorem for a weak solution of fractional parabolic problem by the {Rothe} method},
     journal = {Nanosistemy: fizika, himi\^a, matematika},
     pages = {5--15},
     publisher = {mathdoc},
     volume = {15},
     number = {1},
     year = {2024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/NANO_2024_15_1_a0/}
}
TY  - JOUR
AU  - Y. Bekakra
AU  - A. Bouziani
TI  - Existence and uniqueness theorem for a weak solution of fractional parabolic problem by the Rothe method
JO  - Nanosistemy: fizika, himiâ, matematika
PY  - 2024
SP  - 5
EP  - 15
VL  - 15
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/NANO_2024_15_1_a0/
LA  - en
ID  - NANO_2024_15_1_a0
ER  - 
%0 Journal Article
%A Y. Bekakra
%A A. Bouziani
%T Existence and uniqueness theorem for a weak solution of fractional parabolic problem by the Rothe method
%J Nanosistemy: fizika, himiâ, matematika
%D 2024
%P 5-15
%V 15
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/NANO_2024_15_1_a0/
%G en
%F NANO_2024_15_1_a0
Y. Bekakra; A. Bouziani. Existence and uniqueness theorem for a weak solution of fractional parabolic problem by the Rothe method. Nanosistemy: fizika, himiâ, matematika, Tome 15 (2024) no. 1, pp. 5-15. http://geodesic.mathdoc.fr/item/NANO_2024_15_1_a0/