Simultaneous inversion of the potential term and the fractional orders in a multi-term time-fractional diffusion equation
Liangliang Sun, Y S Li, Yun Zhang
Abstract
Abstract In the present paper, we devote our effort to a nonlinear inverse problem for simultaneously recovering the potential function and the fractional orders in a multi-term time-fractional diffusion equation from the noisy boundary Cauchy data in the one-dimensional case. The uniqueness for the inverse problem is derived based on the analytic continuation, the Laplace transformation and the Gel’fand–Levitan theory. Finally, the Levenberg–Marquardt regularization method with a regularization parameter chosen by a sigmoid-type function is applied for finding a stable approximate solution. Three numerical examples are provided to show the effectiveness of the proposed method.
Topics & Concepts
MathematicsUniquenessRegularization (linguistics)Inverse problemLaplace transformTerm (time)Sigmoid functionContinuationMathematical analysisFractional calculusApplied mathematicsCauchy distributionInverseArtificial neural networkComputer sciencePhysicsMachine learningArtificial intelligenceProgramming languageGeometryQuantum mechanicsFractional Differential Equations SolutionsNumerical methods in engineeringNumerical methods in inverse problems