The Nonlinear Convolutional Equations Solvable in Closed Form

Abstract

„The nonlinear convolutional equations solvable in closed form" Mathematical Modelling Analysis, 2(1), p. 75-78

New polyconvolution product for Fourier‐cosine and Laplace integral operators and their applications

“…In particular, this method can be used to construct the polyconvolution involving the Hankel integral transform [6, 7] and Fourier–Kontorovich–Lebedev integral transforms [8], which leads to the study of the operational properties of polyconvolution and applied to solving some classes of integral equations, and systems of integral equations. In this paper, extending the notions in [5], we introduce a new structure of polyconvolution operator involving the Fourier cosine $$$ \left({F}_c\right) $$$‐Laplace $$$ \left(\mathcal{L}\right) $$$ integral transforms and apply it to study the solvability in closed‐form of classes for integral equations.…”

“…His convolution constructing method is based on factorization equality and can be applied to most convolutions with arbitrary integral transform appearing already in [4]. In the year 1997, Kakichev generalized this approach and introduced the concept of polyconvolution or "generalized convolution" [5], more details as follows.…”