Source term inversion of Caputo-Hadamard fractional diffusion equation on spherically symmetric domain

Abstract

Abstract: The problem of identifying the source term for the Caputo-Hadamard fractional diffusion equation on the spherically symmetric domain is studied. The exact solution to the problem is obtained by using Laplace transform and inverse Laplace transform. Analytical examination of the exact solution reveals that the problem is ill-posed. On this basis, the Quasi-boundary regularization method is used to solve the stability problem of the solution. Furthermore, two convergence error estimates under both a priori regularization parameter selection rule and a posteriori regularization parameter selection rule are provided respectively. The finite difference discretization method is used to obtain the iterative scheme. The effectiveness and stability of the regularization method are demonstrated through numerical examples.

Key words: inverse problem, Caputo-Hadamard fractional diffusion equation, spherically symmetric domain, identifying unknown source, Quasi-boundary regularization method

CLC Number:

O241.1

ZHANG Chen-yu, YANG Fan. Source term inversion of Caputo-Hadamard fractional diffusion equation on spherically symmetric domain[J]. Journal of Lanzhou University of Technology, 2025, 51(5): 154-162.

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