Existence and uniqueness theorem for a weak solution of fractional parabolic problem by the Rothe method
https://doi.org/10.17586/2220-8054-2024-15-1-5-15
Abstract
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, tj). We then evaluate the accuracy of the proposed method to demonstrate that the implemented sequence of α-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.
Supporting agencies: The authors would like to thank the reviewer for his valuable comments and suggestions
About the Authors
Y. Bekakra
ICOSI Laboratory, Abbes Laghrour University
Algeria
Algeria
Department of Mathematics and Informatics.
Laghrour University, Khenchela, 04000
A. Bouziani
ICOSI Laboratory, Abbes Laghrour University; L’arbi Ben M’hidi University
Algeria
Algeria
Department of Mathematics and Informatics, ICOSI Laboratory University; Department of Mathematics, L’arbi Ben M’hidi University
Khenchela, 04000, Algeria; Oum El Bouagui, 04000
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Review
For citations:
Bekakra Y., Bouziani A. Existence and uniqueness theorem for a weak solution of fractional parabolic problem by the Rothe method. Nanosystems: Physics, Chemistry, Mathematics. 2024;15(1):5-15. https://doi.org/10.17586/2220-8054-2024-15-1-5-15
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