Inverse Source Problem for Time Fractional Diffusion Equation With Mittag-Leffler Kernel
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Date
2020
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Springer
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GOLD
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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.
Description
Le Dinh, Long/0000-0001-8805-4588; Nguyen, Huu-Can/0000-0001-6198-1015
Keywords
Atangana-Baleanu Derivative, Ill-Posed Problem, Time Fractional Diffusion Equation, Convergence Estimates, Regularization Method, Artificial intelligence, Inverse Problems in Mathematical Physics and Imaging, Inverse Scattering Theory, Inverse Problems, Epistemology, Mathematical analysis, Tikhonov Regularization, Time fractional diffusion equation, Engineering, Differential equation, QA1-939, FOS: Mathematics, Regularization (linguistics), Anomalous Diffusion Modeling and Analysis, Mathematical Physics, Hadamard transform, Convergence estimates, Time-Fractional Diffusion Equation, Tikhonov regularization, Fractional calculus, Pure mathematics, Partial differential equation, A priori and a posteriori, Applied mathematics, Computer science, FOS: Philosophy, ethics and religion, Fracture Mechanics Modeling and Simulation, Philosophy, Mechanics of Materials, Modeling and Simulation, Ill-posed problem, Physical Sciences, Inverse problem, Kernel (algebra), Uniqueness, Atangana–Baleanu derivative, Well-posed problem, Mathematics, Anomalous Diffusion, Ordinary differential equation, Regularization method, Inverse problems for PDEs, regularization method, time fractional diffusion equation, ill-posed problem, convergence estimates, Atangana-Baleanu derivative, Fractional partial differential equations, Ill-posed problems for PDEs
Fields of Science
02 engineering and technology, 01 natural sciences, 0202 electrical engineering, electronic engineering, information engineering, 0101 mathematics
Citation
Can, Nguyen Huu...et al. (2020). "Inverse source problem for time fractional diffusion equation with Mittag-Leffler kernel", Advances in Difference Equations, Vol. 2020, No.1.
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OpenCitations Citation Count
16
Source
Advances in Difference Equations
Volume
2020
Issue
1
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CrossRef : 2
Scopus : 23
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