Extension of lower and upper solutions approach for generalized nonlinear fractional boundary value problems

Abstract

Our main concern in this study is to present the generalized results to investigate the existence of solutions to nonlinear fractional boundary value problems (FBVPs) with generalized nonlinear boundary conditions. The framework of the presented results relies on the lower and upper solutions approach which allows us to ensure the existence of solutions in a sector defined by well-ordered coupled lower and upper solutions. It is worth mentioning that the presented results unify the existence criteria of certain problems which were treated on a case-by-case basis in the literature. Two examples are supplied to support the results.

Keywords

• Antiperiodic boundary conditions
• Caputo fractional derivative
• Fractional differential equations
• Nonlinear boundary conditions
• Upper and Lower solutions
• Periodic boundary conditions