On Opial-type inequalities via fractional calculus

TL;DR

This paper develops new Opial-type inequalities using fractional calculus and applies these results to generalized Riemann-Liouville integral operators, advancing the theoretical framework for differential equations.

Contribution

It introduces novel Opial-type inequalities within fractional calculus and demonstrates their application to generalized Riemann-Liouville operators.

Findings

New Opial-type inequalities established

Applications to generalized Riemann-Liouville operators demonstrated

Enhanced tools for analyzing differential equations

Abstract

Inequalities play an important role in pure and applied mathematics. In particular, Opial inequality plays a main role in the study of the existence and uniqueness of initial and boundary value problems for differential equations. It has several interesting generalizations. In this work we prove some new Opial-type inequalities, and we apply them to generalized Riemann-Liouville-type integral operators.