Stability of the fractional Volterra integro-differential equation by means of ψ-Hilfer operator

被引：36
|
作者：
Sousa, Jose Vanterler da C. [1 ]
Rodrigues, Fabio G. [2 ]
de Oliveira, Edmundo Capelas [1 ]
机构：
[1] Inst Math Stat & Sci Comp Imecc, Dept Appl Math, Sao Paulo, Brazil
[2] Univ La Serena, Dept Matemat, La Serena, Region De Coqui, Chile
来源：
MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2019年 / 42卷 / 09期
关键词：
Banach fixed-point theorem; fractional Volterra integro-differential equation; fractional Volterra integral equation; Ulam-Hyers stability; psi-Hilfer fractional derivative; DIFFERENTIAL-EQUATIONS; ULAM STABILITY; EXISTENCE; UNIQUENESS;
D O I：
10.1002/mma.5563
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, using the Riemann-Liouville fractional integral with respect to another function and the psi-Hilfer fractional derivative, we propose a fractional Volterra integral equation and the fractional Volterra integro-differential equation. In this sense, for this new fractional Volterra integro-differential equation, we study the Ulam-Hyers stability and, also, the fractional Volterra integral equation in the Banach space, by means of the Banach fixed-point theorem. As an application, we present the Ulam-Hyers stability using the alpha-resolvent operator in the Sobolev space W1,1(R+,C).
引用
收藏
页码：3033 / 3043
页数：11
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