Work

Nonlinear integral inequalities involving Ψ -Hilfer fractional integrals and iterated fractional integrals, with applications to Ψ -Caputo fractional differential equations

Year: 2025

Type: article

Abstract: In this paper, modifications of the well-known desingularization method proposed by the first author are used to derive nonlinear versions of the Henry--Gronwall inequality for integral inequalities with the Ψ -Hilfer fractional integral, as well as nonlinear integral inequalities with iterated Ψ -Hilfer fractional integrals. The results are applied to obtain bounds for solutions of initial value problems for nonlinear Ψ -Caputo fractional differential equations, and sufficient conditions for the non-existence of blowing-up solutions.

Source: Electronic journal of qualitative theory of differential equations

DOI: 10.14232/ejqtde.2025.1.30

Authors: Milan Medved, Michal Pospíšil, Eva Brestovanská

Institutions: Comenius University Bratislava, Slovak Academy of Sciences

Language: English

Topic: Nonlinear Differential Equations Analysis

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: Agentúra na Podporu Výskumu a Vývoja

Awards: G2725337324, Kvalitatívne vlastnosti evolučných úloh z prírodných a technických vied, G5103515450