Unified existence results for nonlinear fractional boundary value problems

Abstract

In this work, we focus on investigating the existence of solutions to nonlinear fractional boundary value problems (FBVPs) with generalized nonlinear boundary conditions. By extending the framework of the technique based on well-ordered coupled lower and upper solutions, we guarantee the existence of solutions in a sector defined by these solutions. One notable aspect of our study is that the proposed approach unifies the existence results for the problems that have previously been discussed separately in the literature. To substantiate these findings, we have added three illustrative examples.

Keywords

• lower and upper solutions
• fractional differential equations
• nonlinear boundary conditions
• hilfer fractional derivative
• periodic boundary conditions
• anti-periodic boundary conditions