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Original research article

Identifying inverse source for diffusion equation with conformable time derivative by Fractional Tikhonov method

Author(s):

Ha Vo Thi Thanh, Hung Ngo Ngoc, Phuong Nguyen Duc*

Faculty of Fundamental Science, Industrial University of Ho Chi Minh City, Ho Chi Minh, Vietnam.

Advances in the Theory of Nonlinear Analysis and its Applications 6(4), 433-450.
Received: March 1, 2022

  

  

  

Accepted: June 5, 2022

  

Published: June 7, 2022

Abstract

In this paper, we study inverse source for diffusion equation with conformable derivative:
\[
C_{0}D_{t}^{(\gamma)}u – \Delta u = \Phi(t)\mathcal{F}(x)
\quad \text{where } 0 < \gamma < 1, \ (x,t) \in \Omega \times (0,T).
\]

We survey the following issues: The error estimate between the sought solution and the regularized solution under a priori parameter choice rule; The error estimate between the sought solution and the regularized solution under a posteriori parameter choice rule; Regularization and $\mathcal{L}_{p}$ estimate by Truncation method.

Keywords: Fractional diffusion equation, Inverse source problem, Conformable derivative, Regularization methods, Fractional Tikhonov method.

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APA Style

Thanh, H. V. T., Hung, N., & Phuong, N. D. (2022). Identifying inverse source for diffusion equation with conformable time derivative by Fractional Tikhonov method. Advances in the Theory of Nonlinear Analysis and its Application6(4), 433-450.