Progress in Fractional Differentiation & Applications

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In this article, we build an approximate solution to an Inverse Problem that consist in finding a function whose Caputo fractional derivative is given. We decompose and project the data in appropriate wavelet subspaces and, by a Galerkin scheme, we calculate the coefficients of the unknown function in the chosen wavelet basis. Based on properties of the operator and of the basis, the scheme is simple, efficient and the errors introduced by the approximation can be handled and controlled. We illustrate the results with an example.

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