Reconstruct the unknown source on the right hand  side of time fractional diffusion equation with Caputo-Hadamard derivative

Ngo Ngoc Hung; Danh Hua Quoc Nam; Dinh Long Le

doi:10.61383/ejam.20242263

Authors

Ngo Ngoc Hung Faculty of Fundamental Science, Industrial University of Ho Chi Minh City, Vietnam https://orcid.org/0000-0002-4380-0257
Danh Hua Quoc Nam Division of Applied Mathematics, Thu Dau Mot University, Binh Duong Province, Vietnam https://orcid.org/0000-0001-6742-2265
Le Dinh Long Falculty of Maths, FPT University HCM Saigon Hi-tech Park, Ho Chi Minh City, Vietnam Corresponding Author https://orcid.org/0000-0001-8805-4588

DOI:

https://doi.org/10.61383/ejam.20242263

Keywords:

Inverse source problem, parabolic equation, regularization method, error estimate

Abstract

The Caputo-Hadamard derivative was used to investigate the problem of functional recovery in this study. This problem is ill-posed, we propose a novel Quasi-reversibility for reconstructing the sought function and show that the regularization solution depends on space. After that, the convergence rates are established under a priori and posterior choice rules of regularization parameters, respectively.

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