(untitled) (European Journal of Pure and Applied Mathematics, 2025)
This study investigates the existence of solutions for nonlinear fractional differential equations of order q (1, 2]. We establish new existence results for the boundary conditions ξ(κ) = α eq 0 and ξ(ω)= β eq 0 by incorporating an intermediate point, extending existing methodologies. Our results rely on fixed point theorems and the contraction principle, which provide a robust framework for analyzing these equations. We also provide several illustrative examples to demonstrate our results, showcasing their relevance in theoretical and applied contexts.