Luc, Nguyen HoangBaleanu, DumitruAgarwal, Ravi P.Long, Le DinhMatematik2022-05-232022-05-232021Luc, Nguyen Hoang...et al. (2021). "Identifying the source function for time fractional diffusion with non-local in time conditions", Computational and Applied Mathematics, Vol. 40, No. 5.2238-36031807-0302https://doi.org/10.1007/s40314-021-01538-yThe diffusion equation has many applications in fields such as physics, environment, and fluid mechanics. In this paper, we consider the problem of identifying an unknown source for a time-fractional diffusion equation in a general bounded domain from the nonlocal integral condition. The problem is non-well-posed in the sense of Hadamard, i.e, if the problem has only one solution, the solution will not depend continuously on the input data. To get a stable solution and approximation, we need to offer the regularization methods. The first contribution to the paper is to provide a regularized solution using the modified fractional Landweber method. Two choices are proposed including a priori and a posteriori parameter choice rules, to estimate the convergence rate of the regularized methods. The second new contribution is to use truncation to give an estimate of L-p for the convergence rate.eninfo:eu-repo/semantics/closedAccessInverse Source ProblemFractional Diffusion ProblemIll-Posed ProblemConvergence EstimatesIntegral ConditionRegularizationArticle40510.1007/s40314-021-01538-y2-s2.0-85107237894WOS:000658188400001Q1Q1