Time fractional IHCP with Caputo fractional derivatives

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Abstract

The numerical solution of the time fractional inverse heat conduction problem (TFIHCP) on a finite slab is investigated in the presence of measured (noisy) data when the time fractional derivative is interpreted in the sense of Caputo. A finite difference space marching scheme with adaptive regularization, using mollification techniques, is introduced. Error estimates are derived for the numerical solution of the mollified problem and several numerical examples of interest are provided.

Keywords

Ill-posed problems
Caputo fractional derivatives
Grünwald–Letnikov fractional derivatives
Time fractional inverse heat conduction problem
Finite differences
Mollification

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