Approximation of fractional integrals of H¨older functions
DOI:
https://doi.org/10.17721/1812-5409.2022/4.2Keywords:
fractional integral, integral sums, approximation, H¨older propertyAbstract
The paper is devoted to the rate of convergence of integral sums of two different types to fractional integrals. The first theorem proves the H¨older property of fractional integrals of functions from various integral spaces. Then we estimate the rate of convergence of the integral sums of two types corresponding to the H¨older functions, to the respective fractional integrals. We illustrate the obtained results by several figures.
Pages of the article in the issue: 18 - 25
Language of the article: English
References
SAMKO S. G., KILBAS A. A., MARICHEV, O. I. (1993). Fractional integrals and derivatives (Vol. 1). Yverdon-les-Bains, Switzerland: Gordon and Breach science.
MISHURA YU. S., HOPKALO O.M., ZHELEZNIAK H.S. (2022). Elements of fractional calculus. Fractional integrals. Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics, No. 1, p. 11-19. DOI: https://doi.org/10.17721/1812-5409.2022/1
ODIBAT, Z. (2006). Approximations of fractional integrals and Caputo fractional derivatives. Applied Mathematics and Computation, 178(2), 527-533.
POOSEH S., ALMEIDA R., TORRES D. F. (2012). Approximation of fractional integrals by means of derivatives. Computers and Mathematics with Applications, 64(10), 3090-3100.
MIN CAI, CHANGPIN LI (2019). Theory and numerical approximations of fractional integrals and derivatives. Society for Industrial and Applied Mathematics.
MIN CAI, CHANGPIN LI (2020). Numerical Approaches to Fractional Integrals and Derivatives: A Review, Mathematics, 8(1), 43. DOI: https://doi.org/10.3390/math8010043
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