Recovering unknown source function for composite fractional relaxation equations
Keywords:
Inverse source problem, regularization method., Caputo fractional derivative, diffusion-wave equation, ill-posed problemAbstract
A backward problem for composite fractional relaxation equations is considered with the Caputo fractional derivative. Based on a spectral problem, the representation of solutions is established. Next, we show the mildly ill-posedness in the Hadamard sense. After that, we show the regularization solution using two regularization methods : the Landweber regularization method and the iterative method. Then, the convergence rate between the exact solution and the regularized solution is provided, under the a priori parameter choice rule.
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