Vitalii Shpakivskyi | Institute of mathematics NASU, Kyiv (original) (raw)

Vitalii Shpakivskyi

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Omran Kouba

Higher Institute of Applied Sciences and Technology (HIAST)

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Papers by Vitalii Shpakivskyi

Complex analysis and operator theory, Jun 18, 2024

$Research paper thumbnail of Conformable fractional derivative in commutative algebras$

Ukraïnsʹkij matematičnij vìsnik, Jun 26, 2023

Trends in Mathematics, 2019

Let An be an arbitrary n-dimensional commutative associative algebra over the field of complex nu... more Let An be an arbitrary n-dimensional commutative associative algebra over the field of complex numbers. Let e1 = 1, e2, e3 be elements of An which are linearly independent over the field of real numbers. We consider monogenic (i.e., continuous and differentiable in the sense of Gateaux) functions of the variable xe1 + ye2 + ze3, where x, y, z are real, and obtain a constructive description of all mentioned monogenic functions by means of holomorphic functions of complex variables. It follows from this description that monogenic functions have Gateaux derivatives of all orders. The relations between monogenic functions and partial differential equations are investigated.

arXiv: Complex Variables, 2015

Let mathbbAnm\mathbb{A}_n^mmathbbAnm be an arbitrary nnn-dimensional commutative associative algebra over the fie... more Let mathbbAnm\mathbb{A}_n^mmathbbAnm be an arbitrary nnn-dimensional commutative associative algebra over the field of complex numbers with mmm idempotents. Let e1=1,e2,ldots,eke_1=1,e_2,\ldots,e_ke1=1,e2,ldots,ek with 2leqkleq2n2\leq k\leq 2n2leqkleq2n be elements of mathbbAnm\mathbb{A}_n^mmathbbAnm which are linearly independent over the field of real numbers. We consider monogenic (i.~e. continuous and differentiable in the sense of Gateaux) functions of the variable sumj=1kxj,ej\sum_{j=1}^k x_j\,e_jsumj=1kxj,ej, where x1,x2,ldots,x_kx_1,x_2,\ldots,x_kx_1,x2,ldots,xk are real, and obtain a constructive description of all mentioned functions by means of holomorphic functions of complex variables. It follows from this description that monogenic functions have Gateaux derivatives of all orders. The present article is generalized of the author's paper [1], where mentioned results are obtained for k=3k=3k=3.

Bulletin de la Société des sciences et des lettres de Łódź, Série: Recherches sur les déformations, 2018

Journal of Mathematical Sciences, 2019

Advances in Applied Clifford Algebras, 2015

arXiv: Complex Variables, 2018

In this paper, we propose a procedure for constructing an infinite number of families of solution... more In this paper, we propose a procedure for constructing an infinite number of families of solutions of given linear differential equations with partial derivatives with constant coefficients. We use monogenic functions that are defined on some sequences of commutative associative algebras over the field of complex numbers. To achieve this goal, we first study the solutions of the so-called characteristic equation on a given sequence of algebras. Further, we investigate monogenic functions on the sequence of algebras and study their relation with solutions of partial deferential equations. The proposed method is used to construct solutions of some equations of mathematical physics. In particular, for the three-dimensional Laplace equation and the wave equation, for the equation of transverse oscillations of the elastic rod and the conjugate equation, a generalized biharmonic equation and the two-dimensional Helmholtz equation. We note that this method yields all analytic solutions of ...

Frontiers in mathematics, 2023

We establish sufficient conditions for the existence of the limiting values of a certain analog o... more We establish sufficient conditions for the existence of the limiting values of a certain analog of the Cauchy type integral taking values in a three-dimensional harmonic algebra with two-dimensional radical.