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Optimal Quadrature Formula for Numerical Integration of Fractional Integrals in a Hilbert Space

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We construct optimal quadrature formulas for numerical integration of the right Riemann–Liouville integrals in the Hilbert space \({W}_{2}^{\left(m,m-1\right)}\left(t,1\right)\). We obtain a system of linear equations for the coefficients of the optimal quadrature formula and establish The existence and uniqueness of its solution. Explicit expressions of the optimal coefficients are obtained.

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Authors and Affiliations

  1. Romanovsky Institute of Mathematics, Academy of Sciences of the Republic of Uzbekistan, 9, University St., 100174, Tashkent, Uzbekistan

    Abdullo Hayotov & Samandar Babaev

  2. Central Asian University, 264, Milliy bog St., 111221, Tashkent, Uzbekistan

    Abdullo Hayotov

  3. Mirzo Ulugbek National University of Uzbekistan, 4, University St., 700174, Tashkent, Uzbekistan

    Abdullo Hayotov

  4. Tashkent International University, 7, Kichik khalka yoli St., 100084, Tashkent, Uzbekistan

    Samandar Babaev

  5. Bukhara State University, 11, M. Ikbol St., 200117, Bukhara, Uzbekistan

    Samandar Babaev

Authors
  1. Abdullo Hayotov
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  2. Samandar Babaev
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Correspondence to Samandar Babaev.

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International Mathematical Schools. Vol. 6. Mathematical Schools in Uzbekistan

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Hayotov, A., Babaev, S. Optimal Quadrature Formula for Numerical Integration of Fractional Integrals in a Hilbert Space. J Math Sci 277, 403–419 (2023). https://doi.org/10.1007/s10958-023-06844-w

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  • DOI: https://doi.org/10.1007/s10958-023-06844-w

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