Karki, Ramesh2025-03-032025-03-032022Karki R. On approximating initial data in some linear evolutionary equations involving fraction Laplacian. Mathematics in Applied Sciences and Engineering. 2022;3(1):1-11. doi:10.5206/mase/13511https://hdl.handle.net/1805/46179We study an inverse problem of recovering the intial datum in a one-dimensional linear equation with Dirichlet boundary conditions when finitely many values (samples) of the solution at a suitably fixed space loaction and suitably chosen finitely many later time instances are known. More specifically, we do this. We consider a one-dimentional linear evolutionary equation invliing a Dirichlet fractional Laplacian and the unknown intial datum f that is assumed to be in a suitable subset of a Sovolev space. Then we investigate how to construct a sequence of future times and choose n so that from n samples taken at a suitably fixed space location and the first n terms of the time sequence we can constrcut an approximation to f with the desired accuracy.en-USAttribution 4.0 InternationalDirichlet fractional LaplacianFourier sine seriesSamplingEvolution equationsAter/future times instancesInitial datumMeasurement algorithmArticle