Hartman-Wintner-type inequality for fractional differential equations with k-Prabhakar derivative | ||||
| Journal of Fractional Calculus and Applications | ||||
| Volume 16, Issue 1, 2025, Page 1-12 PDF (399.83 K) | ||||
| Document Type: Regular research papers | ||||
| DOI: 10.21608/jfca.2025.298382.1113 | ||||
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| Authors | ||||
Narayan Govindrao Abuj  1; Deepak Baburao Pachpatte2
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| 1School of Basic and Applied Sciences, JSPM University Pune | ||||
| 2Department of Mathematics, Dr.Babasaheb Ambedkar Marathwada University,Aurangabad. | ||||
| Abstract | ||||
| 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. | ||||
| Keywords | ||||
| Hartman-Wintner-type inequality; Fractional boundary value problem, nonlocal boundary conditions; k-Prabhakar derivative | ||||
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