Papers by Elina Shishkina
Приложения операторов преобразования типа Векуа – Эрдейи – Лаундеса к дифференциальным уравнениям
Prikladnaâ matematika & fizika, Mar 30, 2024
On the Theory of Spaces of Generalized Bessel Potentials
Siberian Mathematical Journal
Solving the Euler–Poisson–Darboux Equation of Fractional Order
Siberian Mathematical Journal
Comparison of simulation and analytical models for the distribution of a group of agents moving in random directions
Mathematical Methods in the Applied Sciences
The Problem for a Mixed Equation with Fractional Power of the Bessel Operator
Vestnik KRAUNC: Fiziko-Matematičeskie Nauki, Apr 17, 2023
Uniqueness of the Solution of the Cauchy Problem for the General Euler–Poisson–Darboux Equation
Differential Equations, Dec 1, 2022
Mean-Value Theorem for B-Harmonic Functions
Lobachevskii Journal of Mathematics
On the Boundedness of the Generalized Translation Operator on Variable Exponent Lebesgue Spaces
Acta Applicandae Mathematicae
Владикавказский математический журнал
Интерес к уравнениям дробного порядка, как обыкновенным, так и с частнымипроизводными, последние ... more Интерес к уравнениям дробного порядка, как обыкновенным, так и с частнымипроизводными, последние десятилетия неуклонно растет. Это связано с необходимостьюмоделирования процессов, в которых текущее состояние существенно зависит от предыдущихсостояний процесса, т. е. так называемые системы с <<остаточной>> памятью. В работерассматривается задача Коши для одномерного, однородного уравнения Эйлера - Пуассона -Дарбу с дифференциальным оператором дробного порядка по времени, который представляет собойлевосторонний бесселев оператор дробного порядка. При этом, для пространственной переменнойиспользуется обычный дифференциальный оператор второго порядка. Показана связь междупреобразованием Мейера и Лапласа, полученная с использованием преобразования Пуассона,которая представляет собой частный случай соотношения с преобразованием Обрешкова.Доказана теорема, которая определяет условия существования решения рассматриваемой задачи.При доказательстве теоремы существования решения ис...
一般Euler-Poisson-Darboux方程式に対する特異Cauchy問題:一般的Euler-Poisson-Darboux方程式【JST・京大機械翻訳】
Open Mathematics (Web), 2018
Обращение В-потенциалов Рисса в весовых классах функций
A review of the book Direct and Inverse Sturm‐Liouville Problems: A Method of Solution by Vladislav V. Kravchenko Birkhäuser Series Frontiers in Mathematics, 2020, ISBN 978‐3‐030‐47848‐3
Mathematical Methods in The Applied Sciences, 2020
Hyperbolic B-Potentials: Properties and Inversion
General formula of inversion of weighted spherical mean
Прикладная математика & Физика, 2021
Generalized Bessel potential and its application to non-homogeneous singular screened Poisson equation
Integral Transforms and Special Functions, 2020
ABSTRACT In this paper, generalized Bessel potential is studied. A generalization is achieved by ... more ABSTRACT In this paper, generalized Bessel potential is studied. A generalization is achieved by considering the singular Laplace–Bessel operator instead of the Laplace operator in the construction of the Bessel potential. First, we give some auxiliary statements as weighted plane wave relation and generalized Bochner formula. Next, we consider the Bessel kernel and prove some of its properties. After that, we present the definition and properties of generalized Bessel potential. Finally, we consider the generalized Bessel potential as a solution to the singular screened Poisson equation.
Lobachevskii Journal of Mathematics, 2020
Marcel Riesz has created a new method to solve non-homogeneous linear equations, generalizing the... more Marcel Riesz has created a new method to solve non-homogeneous linear equations, generalizing the fractional Riemann-Liouville integral. We generalize and apply this method to solve linear equations with Bessel operators acting with respect to all variables. This method includes the overcoming of difficulties of the theory of differential equations, caused by the occurrence of divergent integrals. Namely, in some cases (for example, for hyperbolic equations), it is necessary to use the analytical continuation of a potential analytically depending on a parameter.
Properties of Mixed Hyperbolic B–Potential
Progress in Fractional Differentiation and Applications, 2018
Mathematical Methods in the Applied Sciences, 2019
The paper is devoted to the study of the fractional integral operator, which is a negative real p... more The paper is devoted to the study of the fractional integral operator, which is a negative real power of the singular wave operator generated by Bessel operator using weighted generalized functions. We give conditions for this operator to be bounded in appropriate spaces, obtain formula for the Hankel transform of this operator, and get formula of connection between this operator and natural degree of singular wave operator generated by Bessel operator.
Mathematical Notes, 2018
A representation for the kernel of the transmutation operator relating a perturbed Bessel equatio... more A representation for the kernel of the transmutation operator relating a perturbed Bessel equation to the unperturbed one is obtained in the form of a functional series with coefficients calculated by a recurrent integration procedure. New properties of the transmutation kernel are established. A new representation of a regular solution of a perturbed Bessel equation is given, which admits a uniform error bound with respect to the spectral parameter for partial sums of the series. A numerical illustration of the application of the obtained result to solve Dirichlet spectral problems is presented.
Integral Representation of Approximating Inverse Operators for Hyperbolic Riesz B -Potential Kernel
Tambov University Reports. Series: Natural and Technical Sciences, 2016
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Papers by Elina Shishkina