In this manuscript, we investigate a non-local fractional boundary
value problem of the form:
(kDγ
ρ,β,ω,a+y)(t) + q(t)y(t) = 0, a < t < b, 2 < β ≤ 3,
y(a) = y′(a) = 0, y′(b) = αy(ξ),
and establish a Hartman-Wintner-type inequality for this problem
within the framework of k-Prabhakar fractional derivatives. By lever
aging the properties of Green's function and its analytical character
istics, we derive the corresponding integral equation for the proposed
nonlocal fractional boundary value problem. The resulting inequality
provides a significant generalization of previous results in the litera
ture [26]. This work broadens the scope of fractional boundary value
problems, offering new insights and laying a foundation for future ap
plications across various fields. The generalization highlighted here
emphasizes the flexibility and depth of the k-Prabhakar framework,
paving the way for further advancements in fractional calculus re
search. Furthermore, this study contributes to both the theoretical
development of fractional calculus and its practical applications in
modeling complex real-world phenomena.