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Reconstructing the right-hand side of the Rayleigh–Stokes problem with nonlocal in time condition

Authors
  • Duc, Phuong Nguyen1
  • Binh, Ho Duy2
  • Long, Le Dinh2
  • Van, Ho Thi Kim2
  • 1 Industrial University of Ho Chi Minh City, Ho Chi Minh City, Vietnam , Ho Chi Minh City (Vietnam)
  • 2 Thu Dau Mot University, Binh Duong Province, Vietnam , Binh Duong Province (Vietnam)
Type
Published Article
Journal
Advances in Difference Equations
Publisher
Springer International Publishing
Publication Date
Oct 23, 2021
Volume
2021
Issue
1
Identifiers
DOI: 10.1186/s13662-021-03626-z
Source
Springer Nature
Keywords
Disciplines
  • Fixed Point Theory and Applications to Fractional Ordinary and Partial Difference and Differential E
License
Green

Abstract

In this paper, the problem of finding the source function for the Rayleigh–Stokes equation is considered. According to Hadamard’s definition, the sought solution of this problem is both unstable and independent of continuous data. By using the fractional Tikhonov method, we give the regularized solutions and then deal with a priori error estimate between the exact solution and its regularized solutions. Finally, the proposed regularized methods have been verified by simple numerical experiments to check error estimate between the sought solution and the regularized solution.

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