Special Session 18: Progress on delay and fractional differential equations with real-world application

An application of the Leray-Schauder nonlinear alternative to a Riemann-Liouville fractional boundary value problem with Lidstone-inspired fractional conditions
Jeffrey Lyons
The Citadel
USA
Co-Author(s):    Jeffrey T. Neugebauer and Aaron Wingo
Abstract:
This paper demonstrates the existence of solutions for a class of nonlinear Riemann--Liouville fractional boundary value problems of order $\alpha+2n$ where $\alpha \in (1,2]$ and $n \in \mathbb{N}$. The conjugate fractional boundary conditions are Lidstone-inspired. The nonlinearity is assumed to be continuous, and we impose suitable growth conditions to establish the existence of solutions. Our approach relies on the construction of a Green`s function using the convolution of the Green`s functions of lower-order fractional boundary value problems and the Leray--Schauder Nonlinear Alternative Theorem.