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

Avyt Asanov , Ricardo Almeida , Agnieszka Malinowska

Abstract

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.
Author Avyt Asanov
Avyt Asanov,,
-
, Ricardo Almeida
Ricardo Almeida,,
-
, Agnieszka Malinowska (FCS / DM)
Agnieszka Malinowska,,
- Department of Mathematics
Journal seriesComputational & Applied Mathematics, [Computational and Applied Mathematics], ISSN 1807-0302, e-ISSN 1807-0302, [0101-8205], (N/A 40 pkt)
Issue year2019
Vol38
No4
Pages1-21
Publication size in sheets1
Keywords in EnglishFractional differential equation, Volterra–Stieltjes integral equation, Generalized midpoint rule
ASJC Classification2604 Applied Mathematics; 2605 Computational Mathematics
DOIDOI:10.1007/s40314-019-0941-2
Internal identifierROC 19-20
Languageen angielski
LicenseJournal (articles only); other; Uznanie Autorstwa (CC-BY); with publication
Score (nominal)40
Score sourcejournalList
ScoreMinisterial score = 40.0, 23-03-2020, ArticleFromJournal
Publication indicators Scopus SNIP (Source Normalised Impact per Paper): 2018 = 0.892; WoS Impact Factor: 2017 = 0.863 (2) - 2017=0.865 (5)
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