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

TL;DR

This paper establishes Lyapunov and Hartman-Wintner inequalities for fractional differential equations with generalized Hilfer derivatives, proving the existence of positive solutions and providing eigenvalue bounds.

Contribution

It introduces new inequalities for nonlinear fractional boundary value problems with generalized Hilfer derivatives, extending classical results.

Findings

Derived Lyapunov-type inequalities for fractional equations

Proved existence of positive solutions under certain conditions

Provided lower bounds for eigenvalues of fractional operators

Abstract

In this work, we obtain a Lyapunov-type and a Hartman-Wintner-type inequalities for a linear and a nonlinear fractional differential equation with generalized Hilfer operator subject to Dirichlet-type boundary conditions. We prove existence of positive solutions to a nonlinear fractional boundary value problem. As an application, we obtain a lower bound for the eigenvalues of corresponding equations.