Quadrature formula for singular integral computation of special type

  • Anis F. Galimyanov Kazan Federal University
  • Almaz F. Gilemzyanov Kazan Federal University
  • Chulpan B. Minnegalieva Kazan Federal University
Keywords: Fractional integral, Riemann-Liouville integral, fractional integration, fractional differentiation, quadrature formula, fractional calculus, singular integral.

Abstract

In this paper we develop the quadrature formula for the singular integral with the Cauchy kernel from the fractional Riemann-Liouville integral. The derivation is based on the quadrature formula obtained previously to calculate the Riemann-Liouville fractional integral. During the development of the quadrature formula to calculate a singular integral with the Cauchy kernel, we use the formulas for the exact calculation of Cauchy type integral principal value. The formula for the remainder of the quadrature formula is derived. The error estimation was performed. A special case of the developed quadrature formula was considered. The calculations were performed in Wolfram Mathematica system.

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Author Biographies

Anis F. Galimyanov, Kazan Federal University

Kazan Federal University

Almaz F. Gilemzyanov, Kazan Federal University

Kazan Federal University

Chulpan B. Minnegalieva, Kazan Federal University

Kazan Federal University

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Published
2018-08-30
How to Cite
Galimyanov, A., Gilemzyanov, A., & Minnegalieva, C. (2018). Quadrature formula for singular integral computation of special type. Amazonia Investiga, 7(15), 69-73. Retrieved from https://amazoniainvestiga.info/index.php/amazonia/article/view/393
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Articles