| 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. |
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