Existence and Uniqueness of Solutions for Initial Value Problem of Nonlinear Fractional Differential Equations

الملخص EN

We discuss the initial value problem for the nonlinear fractional differential equation L(D)u=f(t,u), t∈(0,1], u(0)=0, where L(D)=Dsn-an-1Dsn-1-⋯-a1Ds1, 0

We extend the basic theory of differential equation, the method of upper and lower solutions, and monotone iterative technique to the initial value problem.

Some existence and uniqueness results are established.