Iterative techniques with initial time difference and computer realization for the initial value problem for caputo fractional differential equations

Some algorithms are given and applied in an appropriate computer environment to solve approximately the initial value problem for scalar nonlinear Caputo fractional differential equations on a finite interval. Various schemes for constructing successive approximations are suggested. They do not use Mittag–Leffler functions and as a result the practical application of the algorithms is easier. Several particular initial value problems for Caputo fractional differential equations are given to illustrate the advantages of the iterative techniques.