Existence of Solutions for Fractional Order Differential Equations: Extended Results (European Journal of Pure and Applied Mathematics, 2025)
This study investigates the existence of solutions for nonlinear fractional differential equations of order $ q \in (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.