Progress in Fractional Differentiation & Applications
Article Title
An Inverse Problem for the Caputo Fractional Derivative by Means of the Wavelet Transform
Abstract
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.
Digital Object Identifier (DOI)
http://dx.doi.org/10.18576/pfda/040103
Recommended Citation
A. Fabio, Marcela and I. Troparevsky, Marıa
(2018)
"An Inverse Problem for the Caputo Fractional Derivative by Means of the Wavelet Transform,"
Progress in Fractional Differentiation & Applications: Vol. 4:
Iss.
1, Article 3.
DOI: http://dx.doi.org/10.18576/pfda/040103
Available at:
https://digitalcommons.aaru.edu.jo/pfda/vol4/iss1/3