Inverse source problem for time fractional diffusion equation with Mittag-Leffler kernel
Nguyen Huu Can, Nguyen Hoang Luc, Dumitru Bǎleanu, Yong Zhou, Le Dinh Long
Abstract
Abstract In this work, we study the problem to identify an unknown source term for the Atangana–Baleanu fractional derivative. In general, the problem is severely ill-posed in the sense of Hadamard. We have applied the generalized Tikhonov method to regularize the instable solution of the problem. In the theoretical result, we show the error estimate between the regularized and exact solutions with a priori parameter choice rules. We present a numerical example to illustrate the theoretical result. According to this example, we show that the proposed regularization method is converged.
Topics & Concepts
Tikhonov regularizationMathematicsHadamard transformRegularization (linguistics)Applied mathematicsInverse problemKernel (algebra)Well-posed problemA priori and a posterioriOrdinary differential equationPartial differential equationFractional calculusUniquenessMathematical analysisDifferential equationComputer sciencePure mathematicsEpistemologyPhilosophyArtificial intelligenceFractional Differential Equations SolutionsNumerical methods in engineeringNumerical methods in inverse problems