About the authors
| First name, Middle name, Last name, Scientific degree, Scientific rank, Current position. Full and brief name of the organization, The organization address. | Gorskaya T.Yu. – candidate of technical sciences, associate professor E-mail: This e-mail address is being protected from spambots. You need JavaScript enabled to view it Kazan State University of Architecture and Engineering The organization address: 420043, Russia, Kazan, Zelenaya st., 1 Galimyanov A.F. – candidate of physical-mathematical sciences, associate professor E-mail: This e-mail address is being protected from spambots. You need JavaScript enabled to view it Kazan Federal University The organization address: 420008, Russia, Kazan, Kremlevskaya st., 18 |
| Title of the article | Approximation of fractional integrals by private sums of the Fourier series |
| Abstract. | Problem statement. The purpose of this study is the development and application of approximate methods for calculating integrals, which is the part of the models used by the integrals of Riemann-Liouville and the creation of a software product, allowing to carry out similar calculations for the given functions. Results. Main results of the research consist in the construction of quadrature formulas for the integral, there were cases when the density of the integral is a function from space of continuous functions having generalized derivatives with the weight, and H?lder classes of functions with weight. For the proposed quadrature formulas next, we investigated the error of its approximation in spaces of continuous functions and square-summable with weight functions. The study has efficient error estimates approximation of the apparatus in the proposed classes of functions. In addition an approximate method implemented on a computer in the form of a program in the C language. Conclusions. The significance of the results for the construction industry is that when solving the tasks, including the task of finding shapes of structures, considering material properties, environmental changes, models which use integrals of Riemann-Liouvile, you can apply the approximate approach, the quadrature formula proposed in the article. |
| Keywords. | Riemann-Liouville integrals, Fulier series, quadrature formulas, approximate calculations, error estimates. |
| For citations: | Gorskaya T.Yu., Galimyanov A.F. Approximation of fractional integrals by private sums of the Fourier series // Izvestiya KGASU. 2017. №3(41) P.261-265. |
