# Quadrature formulas for the calculation of the Riemann-Liuville fractional integral

• Anis F. Galimyanov Kazan (Privolzhsky) Federal University
• Almaz F. Gilemzyanov Kazan (Privolzhsky) Federal University
• Chulpan B. Minnegalieva Kazan (Privolzhsky) Federal University
Keywords: Quadrature formula, fractional integration, fractional calculation, fractional Riemann-Liouville integral.

### Abstract

The quadrature formulas for the fractional Riemann-Liouville integral are investigated in this

article. A linear operator is introduced that associates ] , [ ) ( baCx  a polynomial n n P (; x)H

satisfying the condition ( )( ) ( )( ) a n j a j I P x I  x   + + = , n j , 0 = , where j x – are Chebyshev points. The integrand is approximated by an algebraic polynomial. The formula of the remainder term for the quadrature formula is derived. The quadrature formulas obtained are verified using the Wolfram Mathematica computer algebra system.

### Author Biographies

Anis F. Galimyanov, Kazan (Privolzhsky) Federal University

Kazan (Privolzhsky) Federal University

Almaz F. Gilemzyanov, Kazan (Privolzhsky) Federal University

Kazan (Privolzhsky) Federal University

Chulpan B. Minnegalieva, Kazan (Privolzhsky) Federal University

Kazan (Privolzhsky) Federal University

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Published
2018-08-30
How to Cite
Galimyanov, A., Gilemzyanov, A., & Minnegalieva, C. (2018). Quadrature formulas for the calculation of the Riemann-Liuville fractional integral. Amazonia Investiga, 7(15), 74-80. Retrieved from https://amazoniainvestiga.info/index.php/amazonia/article/view/400
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