Along with classical integration and differentiation, the concepts of fractional integral and fractional differential are widely used in modern mathematics. In this work, we construct an optimal quadrature formula for approximating fractional Riemann-Liouville integrals. Here we will construct the optimal quadrature formula by finding the smallest value of the norm of the error functional of the quadrature formula based on the coefficients Cb. First, using the extremal function, we find a representation of the norm of the error functional of the formula. To find the smallest value of the norm of the error functional over the coefficients, we construct the Lagrange function and, taking the partial derivatives from this function over the undetermined coefficients and equating them to zero, we obtain a system of linear equations. We present an algorithm for obtaining an explicit solution to this system based on a discrete analogue of a specific differential operator.
| Mualliflar | Hayotov, A.R., Khaitov, T.O., Buvasherov, D.S., Хаётов, А.Р., Хаитов, Т.О., Бувашеров, Д.С. |
|---|---|
| Jurnal | Ҳисоблаш ва амалий математика муаммолари |
| Nashriyot | Тошкент ахборот технологиялари университети қошидаги, Ахборот-коммуникация технологиялари илмий-инновацион, маркази |
| ISSN | 2181-8460, 2181-046X |
| Nashr sanasi | 2024-12-11 |
| Son | 4/1 |
| Betlar | 142-150 |
| Til | Ingliz |
| Ilmiy soha | Fizika-matematika |
| Indeksga qo‘shilgan | 2026-08-27 |
fractional integral, fractional differential, extremal function, optimal quadrature formula, functional errors, Hilbert space, дробный интеграл, дробный дифференциал, экстремальная функция, оптимальная квадратурная формула, функционал погрешность пространство Гильберта
| APA | Hayotov, A.R., Khaitov, T.O., Buvasherov, D.S., Хаётов, А.Р., Хаитов, Т.О., & Бувашеров, Д.С. (2024). An optimal formula for numerical integration of fractional Riemann-Liouville integral. Ҳисоблаш ва амалий математика муаммолари, (4/1), 142-150. https://journals.airi.uz/index.php/pvpm/article/view/57 |
|---|---|
| GOST (OAK) | Hayotov, A.R. va b. An optimal formula for numerical integration of fractional Riemann-Liouville integral // Ҳисоблаш ва амалий математика муаммолари. – 2024. – № 4/1. – P. 142-150. |
| MLA | Hayotov, A.R., Khaitov, T.O., Buvasherov, D.S., Хаётов, А.Р., Хаитов, Т.О., and Бувашеров, Д.С. “An optimal formula for numerical integration of fractional Riemann-Liouville integral.” Ҳисоблаш ва амалий математика муаммолари, (4/1), 142-150, 2024. https://journals.airi.uz/index.php/pvpm/article/view/57 |
| Chicago | Hayotov, A.R., Khaitov, T.O., Buvasherov, D.S., Хаётов, А.Р., Хаитов, Т.О., and Бувашеров, Д.С. “An optimal formula for numerical integration of fractional Riemann-Liouville integral.” Ҳисоблаш ва амалий математика муаммолари, (4/1), 142-150 (2024). https://journals.airi.uz/index.php/pvpm/article/view/57 |
| Harvard | Hayotov, A.R., Khaitov, T.O., Buvasherov, D.S., Хаётов, А.Р., Хаитов, Т.О., and Бувашеров, Д.С (2024) ‘An optimal formula for numerical integration of fractional Riemann-Liouville integral’, Ҳисоблаш ва амалий математика муаммолари, (4/1), 142-150. https://journals.airi.uz/index.php/pvpm/article/view/57 |
| BibTeX | @article{hayotovar2024,
title = {An optimal formula for numerical integration of fractional Riemann-Liouville integral},
author = {Hayotov, A.R. and Khaitov, T.O. and Buvasherov, D.S. and Хаётов, А.Р. and Хаитов, Т.О. and Бувашеров, Д.С.},
journal = {Ҳисоблаш ва амалий математика муаммолари},
year = {2024},
number = {4/1},
pages = {142-150},
url = {https://journals.airi.uz/index.php/pvpm/article/view/57}
} |
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