Recovering initial condition backward problem for composite fractional relaxation equations

Authors

  • Le Dinh Long Faculty of Information Technology, Industrial University of Ho Chi Minh City, Vietnam
  • Ngo Ngoc Hung Faculty of Fundamental Science, Industrial University of Ho Chi Minh City, Vietnam

DOI:

https://doi.org/10.1234/4v45f027

Keywords:

backward problem, initial data, diffusion-wave equation, Caputo fractional derivative, ill-posed problem, regularization method

Abstract

A backward problem for composite fractional relaxation equations is considered with Caputo's fractional derivative. Based on a spectral problem, the representation of solutions is established. Next, we show the mildly ill-posedness in the Hadamard sense. Afterthat, we show the regularization solution by two regularization methods : the Landweber regularization method and the iterative method. Afterthat, the convergent rate between the exact solution and the regularized solution is provided, under the a priori parameter choice rule.

Additional Files

Published

28-03-2025

Issue

Vol. 3 No. 1 (2025)

Section

Research Article

License

Copyright (c) 2025 Letters on Applied and Pure Mathematics

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Recovering initial condition backward problem for composite fractional relaxation equations. (2025). Letters on Applied and Pure Mathematics, 3(1), 1-10. https://doi.org/10.1234/4v45f027