Yuqiang Feng, Yuanyuan Wang, Deyi Li

Comparison Theorem and Solvability of the Boundary Value Problem of a Fractional Differential Equation

abstract:
When the nonlinearities satisfy the growth conditions on a finite interval, some existence results of solutions to the boundary value problems of fractional differential equations are established via comparison theorem, upper and lower solutions method and fixed point theorems. An example is presented to illustrate the applications of the obtained results.

Mathematics Subject Classification: 26A33, 34B15

Key words and phrases: Comparison theorem, fractional differential equation, upper and lower solutions method, the Banach contraction principle, Shauder's fixed-point theorem