Regional Reconstruction of Semilinear Caputo Type Time-Fractional Systems Using the Analytical Approach

Abstract

The aim of this paper is to investigate the concept of regional observability which is a very important notion of systems theory, precisely regional reconstruction of the initial state for a semilinear Caputo type time-fractional diffusion system which is an interesting class of sytems . Then we give some definitions and properties to introduce our notion. The approaches attempted in this work are both based on fixed point techniques that leads to a successful algorithm which is tested by numerical examples which valid the used approach.