Hartman-Wintner-type inequality for fractional differential equations with k-Prabhakar derivative
Year: 2025
Type: article
Abstract: In this manuscript, we investigate a non-local fractional boundaryvalue problem of the form:(kDγρ,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 problemwithin the framework of k-Prabhakar fractional derivatives. By leveraging the properties of Green’s function and its analytical characteristics, we derive the corresponding integral equation for the proposednonlocal fractional boundary value problem. The resulting inequalityprovides a significant generalization of previous results in the literature [26]. This work broadens the scope of fractional boundary valueproblems, offering new insights and laying a foundation for future applications across various fields. The generalization highlighted hereemphasizes the flexibility and depth of the k-Prabhakar framework,paving the way for further advancements in fractional calculus research. Furthermore, this study contributes to both the theoreticaldevelopment of fractional calculus and its practical applications inmodeling complex real-world phenomena.
Institutions: JSPM University, Dr. Babasaheb Ambedkar Marathwada University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W2786801750