Aprimorando o método de regularização de Tikhonov utilizando um operador diferencial de ordem fracionária

Abstract

Tikhonov regularization is a typical method used to solve ill-posed inverse problems, recom mended when experimental errors in input data are considered. However, for some cases, this technique does not ensure good solutions. In this work, an improvement on the Tikhonov regu larization method was proposed and tested on the black body radiation problem solution. The methodology consists in replacing the differential operator of integer-order, that can be found in the solution of the original functional, for a differential operator of non-integer order. This unprecedent proposal provides more flexibility regarding modeling the solution of interest, due two parameters, λ e α, which is different from the original Tikhonov method. Furthermore, it has a greater solution space when compared to integer differential operators. In this work, it is clearly shown that the differential operator of fractional order provides a better solution than the usual method, even when the presence of experimental error is considered.