426 research outputs found
Anatoly Kuznetsov, Author of Babi Yar: The History of the Book and the Fate of the Author
No full textThis Introduction to the special issue devoted to Anatoly Kuznetsov, author of Babi Yar: A Document in the Form of a Novel, dwells on the different aspects of the book’s importance, surveys the life of the author as intertwined with the history of this book, suggests a way of reading his other work in the light of Babi Yar, and notes the contributions of the articles collected in this issue
The Role of the Mittag-Leffler Function in Fractional Modeling
No full textThis is a survey paper illuminating the distinguished role of the Mittag-Leffler function and its generalizations in fractional analysis and fractional modeling. The content of the paper is connected to the recently published monograph by Rudolf Gorenflo, Anatoly Kilbas, Francesco Mainardi and Sergei Rogosin
Nonlinear differential equations with marchaud‐hadamard‐type fractional derivative in the weighted space of summable functions
No full textThe paper is devoted to the study of the Cauchy‐type problem for the nonlinear differential equation of fractional order 0 < α < 1:
containing the Marchaud‐Hadamard‐type fractional derivative (Dα 0+, μ y)(x), on the half‐axis R+ = (0, +oo) in the space Xp,α c,0 (R+) defined for α > 0 by
where Xp c, 0 (R+) is the subspace of Xp c (R+) of functions g Xp c (R + ) with compact support on infinity: g(x) = 0 for large enough x > R. The equivalence of this problem and of the nonlinear Volterra integral equation is established. The existence and uniqueness of the solution y(x) of the above Cauchy‐type problem is proved by using the Banach fixed point theorem. Solution in closed form of the above problem for the linear differential equation with f[x, y(x)] = λy(x) + f(x) is constructed. The corresponding assertions for the differential equations with the Marchaud‐Hadamard fractional derivative (Dα 0+ y)(x) are presented. Examples are given.
First Published Online: 14 Oct 201
Fractional Calculus of the Generalized Wright Function
No full textMathematics Subject Classification: 26A33, 33C20.The paper is devoted to the study of the fractional calculus of the generalized Wright function
pΨq(z) defined for z ∈ C, complex ai, bj ∈ C and real αi, βj ∈ R (i = 1, 2, · · · p; j = 1, 2, · · · , q) by the series
pΨq (z) It is proved that the Riemann-Liouville fractional integrals and derivative of the Wright function are also the Wright functions but of greater order. Special cases are considered.* The present investigation was partially supported by Belarusian Fundamental Research Fund
The Absurdity of Reality in the Novel of Anatoly Korolev «Byt Boschom» («To be Bosch»)
No full textThe article is devoted to the research of the controversial novel’s poetics of the modern prose writer Anatoly Korolev, the representative of the frontier aesthetics between realism and postmodernism. The author uses various discourses to interpret an absurdity in the novel «Byt Boschom» («To be Bosch»): narration about reality, text in text, metatext. The meaning of the discourses’ combination is represented in the article. Studying the absurdity in the novel allows to see existential problems revealed in this writing
The Absurdity of Reality in the Novel of Anatoly Korolev «Byt Boschom» («To be Bosch»)
No full textThe article is devoted to the research of the controversial novel’s poetics of the modern prose writer Anatoly Korolev, the representative of the frontier aesthetics between realism and postmodernism. The author uses various discourses to interpret an absurdity in the novel «Byt Boschom» («To be Bosch»): narration about reality, text in text, metatext. The meaning of the discourses’ combination is represented in the article. Studying the absurdity in the novel allows to see existential problems revealed in this writing
Fractional Integration of the Product of Bessel Functions of the First Kind
No full textDedicated to 75th birthday of Prof. A.M. Mathai, Mathematical Subject Classification 2010:26A33, 33C10, 33C20, 33C50,
33C60, 26A09Two integral transforms involving the Gauss-hypergeometric function in the kernels are considered. They generalize the classical Riemann-Liouville and Erdélyi-Kober fractional integral operators. Formulas for compositions of such generalized fractional integrals with the product of Bessel functions of the first kind are proved. Special cases for the product of cosine and sine functions are given. The results are established in terms of generalized Lau-ricella function due to Srivastava and Daoust. Corresponding assertions for the Riemann-Liouville and Erdélyi-Kober fractional integrals are presented
Cauchy Problem for Differential Equation with Caputo Derivative
No full textThe paper is devoted to the study of the Cauchy problem for a nonlinear
differential equation of complex order with the Caputo fractional derivative.
The equivalence of this problem and a nonlinear Volterra integral equation
in the space of continuously differentiable functions is established. On the
basis of this result, the existence and uniqueness of the solution of the
considered Cauchy problem is proved. The approximate-iterative method
by Dzjadyk is used to obtain the approximate solution of this problem. Two
numerical examples are given
An Analog of the Tricomi Problem for a Mixed Type Equation with a Partial Fractional Derivative
No full textMathematics Subject Classification 2010: 35M10, 35R11, 26A33, 33C05, 33E12, 33C20.The paper deals with an analog of Tricomi boundary value problem for a partial differential equation of mixed type involving a diffusion equation with the Riemann-Liouville partial fractional derivative and a hyperbolic equation with two degenerate lines. By using the properties of the Gauss hypergeometric function and of the generalized fractional integrals and derivatives with such a function in the kernel, the uniqueness and existence of a solution of the considered problem are proved, and its explicit solution is established in terms of the new special function
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