Abstract:

The Caputo fractional differential equations Dn*0y(x)=f(x,y(x)) with initial value conditions are investigated, where n∈(0,1) and the function f(x,y(x)) meets some integrable conditions. Existence and uniqueness results of solutions are obtained by the method of successive approximations under some weak conditions. An example is given to illustrate the results at last.
 

Key words: Caputo fractional differential operators; initial value problems; existence; uniqueness; Picard successive approximations