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The multiple composition of the left and right fractional Riemann-Liouville integrals - analytical and numerical calculations

Ciesielski Mariusz (Czestochowa University of Technology, Institute of Computer and Information Sciences, Czestochowa, Poland)
Blaszczyk Tomasz (Czestochowa University of Technology, Institute of Mathematics, Czestochowa, Poland)

New fractional integral operators of order α  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.

Keywords: fractional calculus, fractional integral operators, numerical algorithms