Abstract
In this paper, we study the existence of solutions for a class of nonlinear higher-order fractional differential equation with fractional nonlocal boundary condition by using the monotone iterative technique based on the method of upper and lower solutions and give a specific iterative equation about its solutions.
Highlights
We consider the existence of solutions for the following nonlinear fractional differential equation with nonlocal boundary value condition:
For more details about fractional calculus and fractional differential equations, we refer the reader to the monographs by Miller and Ross [ ], Heikkila et al [ ], Podlubny [ ], Hilfer [ ], and Kilbas et al [ ], the survey by Agarwal et al [ ], and the papers [ – ]
Many scholars have studied the existence for nonlinear fractional differential equations with a variety of boundary conditions; see [ – ] and the references therein
Summary
We consider the existence of solutions for the following nonlinear fractional differential equation with nonlocal boundary value condition: Many scholars have studied the existence for nonlinear fractional differential equations with a variety of boundary conditions; see [ – ] and the references therein. Let ACn be the Banach space of all absolutely continuous functions u(t) on I differentiable up to order n with norm u
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