Lyapunov and Hartman-Wintner type inequalities for a nonlinear\n fractional boundary value problem with generalized Hilfer derivative

2017/02/20 by Mokhtar Kirane, Kirane, Mokhtar, Berikbol T. Torebek +1
Engineering · Mathematics · #26D10 #47J20 #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Differential Equations Analysis #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1702.06073

openalex publication_date 2017/02/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this work, we obtain a Lyapunov-type and a Hartman-Wintner-type\ninequalities for a linear and a nonlinear fractional differential equation with\ngeneralized Hilfer operator subject to Dirichlet-type boundary conditions. We\nprove existence of positive solutions to a nonlinear fractional boundary value\nproblem. As an application, we obtain a lower bound for the eigenvalues of\ncorresponding equations.\n

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