Boundary value problems for Caputo fractional differential equations with nonlocal and fractional integral boundary conditions

摘要

In this paper, we study the existence and uniqueness of solutions for fractional differential equations with nonlocal and fractional integral boundary conditions. New existence and uniqueness results are established using the Banach contraction principle. Other existence results are obtained using O’Regan fixed point theorem and Burton and Kirk fixed point. In addition, an example is given to demonstrate the application of our main results.