In this work, we seek conditions for the existence or nonexistence of solutions for nonlinear Riemann-Liouville fractional boundary value problems of order \ (+ 2n\), where \ ( (m-1, m]\) with \ (m 3\) and \ (m, n N\). The problem’s nonlinearity is continuous and also depends on a positive parameter upon which our constraints are established. Our approach involves constructing a Green’s function by combining the Green’s functions of a lower-order fractional boundary value problem and a right-focal boundary value problem \ (n\) times. Leveraging the properties of this Green’s function, we apply Krasnosel’skii’s Fixed Point Theorem to establish our results. Several examples are presented to illustrate the existence and nonexistence regions.
Jeffrey W. Lyons (Sat,) studied this question.