Lyapunov-type inequalities for nonlinear fractional differential equations involving Caputo-type operators

Mohseni, Elaeh; Babakhani, Azizollah; Agahi, Hamzeh

doi:10.22124/jmm.2026.32702.2972

Lyapunov-type inequalities for nonlinear fractional differential equations involving Caputo-type operators

Articles in Press

Document Type : Research Article

Authors

¹ Department of Mathematics, Babol Noshirvani University of Technology

² Department of Mathematics, Faculty of Basic Sciences, Babol Noshirnani University of Technology, Babol, Iran

³ Department of Mathematics, Babol Noshirvani oUniversity of Technology

10.22124/jmm.2026.32702.2972

Abstract

This manuscript is devoted to the derivation of Lyapunov-type inequalities by means of a new approach for nonlinear fractional differential problems involving Caputo fractional operators subject to two boundary conditions. The considered problem involves multiple $\psi$-Laplacian operators of the form
\begin{equation*}
{}^CD^\alpha_{\eta^+}\Big[\psi_{2}\Big(\frac{d}{dx}\big(\psi_{1}(\frac{d}{dx}w)\big)\Big)\Big]+p(x)g(w)=0,
\end{equation*}
where $\psi_2$ and $\psi_1$ are odd, increasing functions, $\psi_1$ is sub-multiplicative and $\frac{1}{\psi_1}$ is convex and $g$ is a continuous function. Our results apply $p_+$ and $p_-$, as opposed to $|p|$ which appears in most results in the literature

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