(untitled) (European Journal of Pure and Applied Mathematics, 2025)
This study introduces a novel class of fractional differential equations characterized by antiperiodic parametric boundary conditions of order µ 2 (2; 3]. The parameters θ and ξ play a crucial role in shaping the boundary conditions by defining specific values and functional behavior. By employing fixed point theorems, we establish existence results for a fractional differential equation equipped with nonlocal antiperiodic boundary conditions involving a Caputo fractional derivative at one of the boundaries. Our investigation centers on a nonlocal point 0 ≤ θ < b, in conjunction with a fixed endpoint at the interval’s extremity (0; b]. This approach enables us to extend the interval of interest to (-1; b]. The findings presented in this study serve to expand and generalize the existing body of knowledge pertaining to nonlocal and classical fractional differential equations.