Fórmula quadratura para computação integral singular de tipo especial
Palavras-chave:
Integral fracionário, integral de Riemann-Liouville, integração fracional, diferenciação fracional, fórmula de quadratura, cálculo fracionário, integral singular.Resumo
Fórmula para a integral singular com o núcleo de Cauchy da integral fracionária de Riemann-Liouville. A derivação é baseada na fórmula de quadratura obtida anteriormente para calcular a integral fracional de Riemann-Liouville. Durante o desenvolvimento da fórmula de quadratura para calcular uma integral singular com o kernel de Cauchy, usamos as fórmulas para o cálculo exato do valor principal integral do tipo Cauchy. A fórmula para o restante da fórmula de quadratura é derivada. A estimativa de erro foi realizada. Um caso especial da fórmula de quadratura desenvolvida foi considerado. Os cálculos foram realizados no sistema Wolfram Mathematica.
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Referências
Agarwal, P; Nieto, JJ; Luo, MJ. (2017). Extended Riemann-Liouville type fractional derivative operator with applications// OPEN MATHEMATICS. 15, 1667-1681
Galimyanov, A. F.; Gilemzyanov, A. F.; Minnegalieva, C. B. (2017). SQUARE FORMULAS FOR WEIL FRACTIONAL INTEGRAL BASED ON TRIGONOMETRIC POLYNOM // JOURNAL OF FUNDAMENTAL AND APPLIED SCIENCES. 9, 1934 – 1944
Golovchun A., Karimova B., Zhunissova M., Ospankulova G., Mukhamadi K. (2017). Content And Language Integrated Learning In Terms Of Multilingualism: Kazakhstani Experience, Astra Salvensis, Supplement No. 10, p. 297-306.
Gorskaya T.Yu., Galimyanov A.F. (2014). Generalized Bubnov-Galerkin method for the equations with a fractional-integral operator / Bulletin from KGASU, ?4 (30). Kazan, pp. 341- 345.
Gorskaya T.Yu., Galimyanov A.F. (2017). Approximation of fractional integrals by partial sums of Fourier series / KGASU Bulletin, ?3 (41). Kazan, pp. 261-265.
Grinko A.P., A.A. Kilbas. (2007). Integral equation of Abel type and local fractional integrals and derivatives, BSU Bulletin. SERIES 1, Physics. Mathematics. Informatics, Minsk, 1, 71- 77.
Labora, DC; Rodriguez-Lopez, R. (2017). FROM FRACTIONAL ORDER EQUATIONS TO INTEGER ORDER EQUATIONS// FRACTIONAL CALCULUS AND APPLIED ANALYSIS. 20(6), 1405-1423
Li, Y; Xiao, W. (2017). FRACTAL DIMENSION OF RIEMANN-LIOUVILLE FRACTIONAL INTEGRAL OF CERTAIN UNBOUNDED VARIATIONAL CONTINUOUS FUNCTION // FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY. 25(5), 1750047
Micula, S. (2018). An iterative numerical method for fractional integral equations of the second kind // JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS. 339, 124-133
Parovik R.I. (2017). Fractional calculus in the theory of oscillatory systems // Modern science-intensive technologies. 1, pp. 61-68.
Pshu A.V. (2017). The solution of the multidimensional integral Abel equation of the second kind with partial fractional integrals // Differential equations. 53 (9), 1195
Villalobos Antúnez, J.V., Popper K.R. (2017). Heráclito y la invención del logos. Un contexto para la Filosofía de las Ciencias Sociales, Opción, vol. 33, núm. 84, diciembre, pp. 4-11.
Zhu, SG; Fan, ZB; Li, G. (2018). APPROXIMATE CONTROLLABILITY OF RIEMANN-LIOUVILLE FRACTIONAL EVOLUTION EQUATIONS WITH INTEGRAL CONTRACTOR ASSUMPTION // JOURNAL OF APPLIED ANALYSIS AND COMPUTATION. 8 (2), 532-548.
Galimyanov, A. F.; Gilemzyanov, A. F.; Minnegalieva, C. B. (2017). SQUARE FORMULAS FOR WEIL FRACTIONAL INTEGRAL BASED ON TRIGONOMETRIC POLYNOM // JOURNAL OF FUNDAMENTAL AND APPLIED SCIENCES. 9, 1934 – 1944
Golovchun A., Karimova B., Zhunissova M., Ospankulova G., Mukhamadi K. (2017). Content And Language Integrated Learning In Terms Of Multilingualism: Kazakhstani Experience, Astra Salvensis, Supplement No. 10, p. 297-306.
Gorskaya T.Yu., Galimyanov A.F. (2014). Generalized Bubnov-Galerkin method for the equations with a fractional-integral operator / Bulletin from KGASU, ?4 (30). Kazan, pp. 341- 345.
Gorskaya T.Yu., Galimyanov A.F. (2017). Approximation of fractional integrals by partial sums of Fourier series / KGASU Bulletin, ?3 (41). Kazan, pp. 261-265.
Grinko A.P., A.A. Kilbas. (2007). Integral equation of Abel type and local fractional integrals and derivatives, BSU Bulletin. SERIES 1, Physics. Mathematics. Informatics, Minsk, 1, 71- 77.
Labora, DC; Rodriguez-Lopez, R. (2017). FROM FRACTIONAL ORDER EQUATIONS TO INTEGER ORDER EQUATIONS// FRACTIONAL CALCULUS AND APPLIED ANALYSIS. 20(6), 1405-1423
Li, Y; Xiao, W. (2017). FRACTAL DIMENSION OF RIEMANN-LIOUVILLE FRACTIONAL INTEGRAL OF CERTAIN UNBOUNDED VARIATIONAL CONTINUOUS FUNCTION // FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY. 25(5), 1750047
Micula, S. (2018). An iterative numerical method for fractional integral equations of the second kind // JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS. 339, 124-133
Parovik R.I. (2017). Fractional calculus in the theory of oscillatory systems // Modern science-intensive technologies. 1, pp. 61-68.
Pshu A.V. (2017). The solution of the multidimensional integral Abel equation of the second kind with partial fractional integrals // Differential equations. 53 (9), 1195
Villalobos Antúnez, J.V., Popper K.R. (2017). Heráclito y la invención del logos. Un contexto para la Filosofía de las Ciencias Sociales, Opción, vol. 33, núm. 84, diciembre, pp. 4-11.
Zhu, SG; Fan, ZB; Li, G. (2018). APPROXIMATE CONTROLLABILITY OF RIEMANN-LIOUVILLE FRACTIONAL EVOLUTION EQUATIONS WITH INTEGRAL CONTRACTOR ASSUMPTION // JOURNAL OF APPLIED ANALYSIS AND COMPUTATION. 8 (2), 532-548.
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Publicado
2018-08-30
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Galimyanov, A. F., Gilemzyanov, A. F., & Minnegalieva, C. B. (2018). Fórmula quadratura para computação integral singular de tipo especial. Amazonia Investiga, 7(15), 69–73. Recuperado de https://amazoniainvestiga.info/index.php/amazonia/article/view/393
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