Weakly singular Gronwall inequalities and applications to fractional differential equations

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:471

Article

Webb, J. R. L.¹ 

[1] Univ Glasgow, Sch Math & Stat, Glasgow G12 8SQ, Lanark, Scotland

关键词: Gronwall inequality;    Volterra integral equation;    Weakly singular kernel;    Fractional differential equation;   

DOI  :  10.1016/j.jmaa.2018.11.004

来源: Elsevier

【 摘 要 】

We obtain some new Gronwall type inequalities which are applicable to some weakly singular Volterra integral equations similar to the ones first studied by D. Henry. The main interest is that we consider cases with a double singularity and we obtain explicit L-infinity bounds rather than L-1 bounds. Furthermore our bounds involve the exponential function and not the Mittag-Leffler function as in some previous works. We give applications to some Volterra integral equations with a doubly singular kernel that arise from Caputo fractional differential equations where, as opposed to previous papers, we have a singularity in the nonlinearity. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free