Open AccessThe multiple composition of the left and right fractional Riemann-Liouville integrals - analytical and numerical calculations
Author(s) -
Mariusz Ciesielski,
Tomasz Błaszczyk
Publication year - 2017
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil1719087c
Subject(s) - mathematics , fractional calculus , order (exchange) , order of integration (calculus) , numerical analysis , mathematical analysis , composition (language) , philosophy , finance , economics , linguistics
New fractional integral operators of order ? ? R+ are introduced. These operators are defined as the composition of the left and right (or the right and left) Riemann-Liouville fractional order integrals. Some of their properties are studied. Analytical results of fractional integrals of several functions are presented. For a numerical calculation of fractional order integrals, two numerical procedures are given. In the final part of this paper, examples of numerical evaluations of these operators of three different functions are shown in plots and the comparison of the numerical accuracy was analyzed in tables.