Problèmes inverses régis par des équations aux dérivées fractionnaires locales

Abstract

In this thesis, we consider an inverse time-dependent source problem for a time-fractional telegraph equation with mixed boundary conditions and an additional measurement at a fixed point. The frac tional derivative is described in the conformable sense. Under some assumptions on the input data, the well-posedness of this inverse problem is shown by using Fourier’s method and Banach’s contraction mapping principle. An inverse space-dependent source problem for a time-fractional telegraph equation with periodic boundary conditions and an additional condition at final time is considered. The fractional derivative is also in the conformable sense. The well-posedness of this inverse problem is shown under some assumptions on the input data by using Fourier’s method. The algorithm using the finite difference method is presented to solve the first inverse problem.