In this book, we describe the definition and the properties of fractional derivative and fractional integral and the approximation methods of fractional derivative and give the solutions of some time-fractional diffusion equations by the difference method.The main aspects of the analysis of difference equations are stability, convergence and error estimations.The essential difference from the other books is that for some fractional diffusion equations with nonlocal boundary conditions as well as ones with classical boundary conditions, stability and error estimates of the difference equations in uniform and graded grids, respectively, are given and computational examples are given to show the validity of the theory.

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