A strategy for inverse source term and the initial data for the time-fractional diffusion equation for the Hyper Bessel operator

Viet Tri Vo

doi:10.61383/ejam.202534117

Authors

Vo Viet Tri Thu Dau Mot University, Ho Chi Minh City, Vietnam https://orcid.org/0000-0003-4830-4954

DOI:

https://doi.org/10.61383/ejam.202534117

Keywords:

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

Abstract

In this paper, we investigate the inverse problem of simultaneously identifying the source term and the initial value for a time-fractional diffusion equation involving a Caputo-like hyper-Bessel operator. We first establish the ill-posedness of the problem and derive a conditional stability estimate. To overcome this difficulty, we apply the modified Fractional Landweber regularization method and provide error estimates under a priori parameter choice rules.

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