THE CONDITIONAL STABILITY AND AN ITERATIVE REGULARIZATION METHOD FOR A FRACTIONAL INVERSE ELLIPTIC PROBLEM OF TRICOMI-GELLERSTEDT-KELDYSH TYPE
Copyright policy )THE CONDITIONAL STABILITY AND AN ITERATIVE REGULARIZATION METHOD FOR A FRACTIONAL INVERSE ELLIPTIC PROBLEM OF TRICOMI-GELLERSTEDT-KELDYSH TYPE
The present paper is devoted to identifying an inaccessible boundary condition for a fractional elliptic problem of Tricomi-Gellerstedt-Keldysh-type. Using the expansion Fourier method, the considered problem can be reformulated as an operator equation of the first kind. To construct a stabilized approximate solution we employ a variant of the iterative method. We also present error estimates between the exact solution and the regularized solution by the a priori and the a posteriori parameter choice rules. Finally, some numerical verifications on the efficiency and accuracy of the proposed algorithm is presented.
- University of Guelma Algeria
- École Nationale Polytechnique d'Oran Algeria
- Badji Mokhtar University Algeria
- University of Skikda Algeria
Inverse problems for PDEs, Artificial intelligence, fractional elliptic equations, Inverse Problems in Mathematical Physics and Imaging, Geometry, Numerical solution to inverse problems in abstract spaces, Mathematical analysis, ill-posed problems, iterative regularization method, Machine learning, QA1-939, FOS: Mathematics, Regularization (linguistics), Stability (learning theory), Biology, Mathematical Physics, Anomalous Diffusion Modeling and Analysis, Ecology, inverse problems, a posteriori parameter choice rule, Applied Mathematics, Applied mathematics, Fractional partial differential equations, Computer science, Nonlocal Partial Differential Equations and Boundary Value Problems, Regularization Methods, Modeling and Simulation, FOS: Biological sciences, Physical Sciences, Ill-posed problems for PDEs, Tricomi-Gellerstedt-Keldysh equations, Inverse, Type (biology), Functional-differential equations with fractional derivatives, Mathematics
Inverse problems for PDEs, Artificial intelligence, fractional elliptic equations, Inverse Problems in Mathematical Physics and Imaging, Geometry, Numerical solution to inverse problems in abstract spaces, Mathematical analysis, ill-posed problems, iterative regularization method, Machine learning, QA1-939, FOS: Mathematics, Regularization (linguistics), Stability (learning theory), Biology, Mathematical Physics, Anomalous Diffusion Modeling and Analysis, Ecology, inverse problems, a posteriori parameter choice rule, Applied Mathematics, Applied mathematics, Fractional partial differential equations, Computer science, Nonlocal Partial Differential Equations and Boundary Value Problems, Regularization Methods, Modeling and Simulation, FOS: Biological sciences, Physical Sciences, Ill-posed problems for PDEs, Tricomi-Gellerstedt-Keldysh equations, Inverse, Type (biology), Functional-differential equations with fractional derivatives, Mathematics
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