A GRONWALL INEQUALITY AND THE CAUCHY-TYPE PROBLEM BY MEANS OF ψ-HILFER OPERATOR

被引：118

作者：

Da Costa Sousa, Jose Vanterler ^{[1
]}

De Oliveira, Edmundo Capelas ^{[1
]}

机构：

[1] Univ Estadual Campinas, UNICAMP, Inst Math Stat & Sci Computat, Dept Appl Math, Rua Sergio Buarque Holanda 651, BR-13083859 Campinas, SP, Brazil

来源：

DIFFERENTIAL EQUATIONS & APPLICATIONS | 2019年 / 11卷 / 01期

关键词：

psi-Hilfer fractional derivative; Cauchy-type problem; existence and uniqueness; continuous dependence; generalized Gronwall inequality; UNIQUENESS; EXISTENCE; STABILITY;

D O I：

10.7153/dea-2019-11-02

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we propose a generalized Gronwall inequality through the fractional integral with respect to another function. The Cauchy-type problem for a nonlinear differential equation involving the psi-Hilfer fractional derivative and the existence and uniqueness of solutions are discussed. Finally, through generalized Gronwall inequality, we prove the continuous dependence of data on the Cauchy-type problem.

引用

页码：87 / 106

页数：20

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