Stanislav Lukashchuk - Academia.edu (original) (raw)
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Homi Bhabha National Institute (HBNI, BARC, MUMBAI)
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Papers by Stanislav Lukashchuk
Построено мультипольное разложение фундаментального решения дробной степени оператора Лапласа чер... more Построено мультипольное разложение фундаментального решения дробной степени оператора Лапласа через многочлены Гегенбауэра. На основе построенного разложения и идеи быстрого метода мультиполей предложен численный алгоритм решения дробно-дифференциального обобщения уравнения Пуассона в двумерном и трехмерном пространствах.
Lobachevskii Journal of Mathematics, 2021
Abstract A problem of functions factorization is studied with respect to the fundamental solution... more Abstract A problem of functions factorization is studied with respect to the fundamental solution of a fractional generalization of the Helmholtz equation. A factorization technique that is applicable for a wide class of functions represented by the Mellin–Barnes type integral is proposed. Factorized representations in integral form and in terms of the H-function are obtained for the fundamental solution of the considered equation.
A nonlinear two-dimensional orthotropic filtration equation with the Riemann–Liouville time-fract... more A nonlinear two-dimensional orthotropic filtration equation with the Riemann–Liouville time-fractional derivative is considered. It is proved that this equation can admits only linear autonomous groups of point transformations. The Lie point symmetry group classification problem for the equation in question is solved with respect to coefficients of piezoconductivity. These coefficients are assumed to be functions of the square of the pressure gradient absolute value. It is proved that if the order of fractional differentiation is less than one then the considered equation with arbitrary coefficients admits a four-parameter group of point transformations in orthotropic case, and a five-parameter group in isotropic case. For the power-law piezoconductivity, the group admitted by the equation is five-parametric in orthotropic case, and six-parametric in isotropic case. Also, a special case of power function of piezoconductivity is determined for which there is an additional extension o...
Построено мультипольное разложение фундаментального решения дробной степени оператора Лапласа чер... more Построено мультипольное разложение фундаментального решения дробной степени оператора Лапласа через многочлены Гегенбауэра. На основе построенного разложения и идеи быстрого метода мультиполей предложен численный алгоритм решения дробно-дифференциального обобщения уравнения Пуассона в двумерном и трехмерном пространствах.
Lobachevskii Journal of Mathematics, 2021
Abstract A problem of functions factorization is studied with respect to the fundamental solution... more Abstract A problem of functions factorization is studied with respect to the fundamental solution of a fractional generalization of the Helmholtz equation. A factorization technique that is applicable for a wide class of functions represented by the Mellin–Barnes type integral is proposed. Factorized representations in integral form and in terms of the H-function are obtained for the fundamental solution of the considered equation.
A nonlinear two-dimensional orthotropic filtration equation with the Riemann–Liouville time-fract... more A nonlinear two-dimensional orthotropic filtration equation with the Riemann–Liouville time-fractional derivative is considered. It is proved that this equation can admits only linear autonomous groups of point transformations. The Lie point symmetry group classification problem for the equation in question is solved with respect to coefficients of piezoconductivity. These coefficients are assumed to be functions of the square of the pressure gradient absolute value. It is proved that if the order of fractional differentiation is less than one then the considered equation with arbitrary coefficients admits a four-parameter group of point transformations in orthotropic case, and a five-parameter group in isotropic case. For the power-law piezoconductivity, the group admitted by the equation is five-parametric in orthotropic case, and six-parametric in isotropic case. Also, a special case of power function of piezoconductivity is determined for which there is an additional extension o...