Numerical solution of some initial-boundary value problems for fractional diffusion and diffusion-wave equations

In the first chapter of this thesis, some basic definitions and theorems related to the concept of fractional derivative are given. In the second chapter, some numerical approximation methods are discussed for fractional derivatives. In the third chapter, numerical solution of an initial-boundary value problem for a time fractional differential equation with order 0<α<1 is investigated. In the fourth chapter, approximate solution of an initial-boundary value problem for a fractional wave equation with 1<α<2 is obtained. The algorithms developed for this purpose are tested on some model examples. The obtained analytical and numerical solutions are compared with tables and graphs. The final chapter presents the conclusion of the study and provides suggestions for potential future research directions.