Fractional differential equations and Volterra-Stieltjes integral equations of the second kind

被引：6

作者：

Asanov, Avyt ^{[1
]}

Almeida, Ricardo ^{[2
]}

Malinowska, Agnieszka B. ^{[3
]}

机构：

[1] Kyrgyz Turkish Manas Univ, Dept Math, Bishkek 720038, Kyrgyzstan

[2] Univ Aveiro, Dept Math, Ctr Res & Dev Math & Applicat CIDMA, P-3810193 Aveiro, Portugal

[3] Bialystok Tech Univ, Fac Comp Sci, PL-15351 Bialystok, Poland

来源：

COMPUTATIONAL & APPLIED MATHEMATICS | 2019年 / 38卷 / 04期

关键词：

Fractional differential equation; Volterra-Stieltjes integral equation; Generalized midpoint rule; NUMERICAL-METHODS; EVOLUTION; RESPECT;

D O I：

10.1007/s40314-019-0941-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we construct a method to find approximate solutions to fractional differential equations involving fractional derivatives with respect to another function. The method is based on an equivalence relation between the fractional differential equation and the Volterra-Stieltjes integral equation of the second kind. The generalized midpoint rule is applied to solve numerically the integral equation and an estimation for the error is given. Results of numerical experiments demonstrate that satisfactory and reliable results could be obtained by the proposed method.

引用

页数：21

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