On approximating initial data in some linear evolutionary equations involving fraction Laplacian

We study an inverse problem of recovering the intial datum in a one-dimensional linear equation with Dirichlet boundary conditions when finitely many values (samples) solution at suitably fixed space loaction and chosen later time instances are known. More specifically, we do this. consider one-dimentional evolutionary invliing fractional Laplacian unknown f that is assumed to be suitable subset Sovolev space. Then investigate how construct sequence future times choose n so from samples taken location first terms can constrcut approximation desired accuracy.