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

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 e...

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Bibliographic Details
Published in:Computational & applied mathematics 2019-12, Vol.38 (4), p.1-21, Article 160
Main Authors: Asanov, Avyt, Almeida, Ricardo, Malinowska, Agnieszka B.
Format: Article
Language:English
Subjects:
Applications of Mathematics
Applied physics
Computational mathematics
Computational Mathematics and Numerical Analysis
Differential equations
Integral equations
Mathematical Applications in Computer Science
Mathematical Applications in the Physical Sciences
Mathematics
Mathematics and Statistics
Stieltjes integral
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Summary: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.
ISSN:2238-3603
1807-0302
DOI:10.1007/s40314-019-0941-2