Monotone Iterative Method for Fractional Differential Equations with Integral Boundary Conditions

Abstract EN

In this paper, the existence of extremal solutions for fractional differential equations with integral boundary conditions is obtained by using the monotone iteration technique and the method of upper and lower solutions.

The main equations studied are as follows: −D0+αut=ft,ut, t∈0,1,u0=0, u1=∫01utdAt, where D0+α is the standard Riemann–Liouville fractional derivative of order α∈1,2 and At is a positive measure function.

Moreover, an example is given to illustrate the main results.