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Using a binary representation for basis elements of an algebra combined with a framework of multiplier and index functions, a connection has been established between the structure of a large class of algebras and the XOR componentwise…
We introduce a fractional magnetic pseudorelativistic operator for a general fractional order $s\in(0,1)$. First we define a suitable functional setting and we prove some fundamental properties. Then we show the behavior of the operator as…
In this paper, we have defined bicomplex valued functions of bounded variations and rectifiable hyperbolic path. We have studied the integration of product-type bicomplex functions over rectifiable hyperbolic path. Also we have established…
The $S$-functional calculus is based on the theory of slice hyperholomorphic functions and it defines functions of $n$-tuples of not necessarily commuting operators or of quaternionic operators. This calculus relays on the notion of…
We discuss the notion of the orbifold transform, and illustrate it on simple examples. The basic properties of the transform are presented, including transitivity and the exponential formula for symmetric products. The connection with the…
We introduce two types bilateral zeta functions, which are related to the primitive and normalized multiple sine functions respectively. Further, we establish their main properties, that is, Fourier expansions, analytic continuations,…
Some differential implications of classical Marx-Strohh\"acker theorem are extended for multivalent functions. These results are also generalized for functions with fixed second coefficient by using the theory of first order differential…
We consider multiply periodic functions, sometimes called Abelian functions, defined with respect to the period matrices associated with classes of algebraic curves. We realise them as generalisations of the Weierstras P-function using two…
In the paper, by virtue of expansions of two finite products of finitely many square sums, with the aid of series expansions of composite functions of (hyperbolic) sine and cosine functions with inverse sine and cosine functions, and in the…
The mean flux theorems are proved for solutions of the Helmholtz equation and its modified version. Also, their converses are considered along with some other properties which generalise those that guarantee harmonicity.
In this communication, one shows that there exists in the literature a certain form of deformed derivative that can here be identified as the dual of conformable derivative. The deformed subtraction is used here, together with the duality…
In the research, with aid of the Fa\`a di Bruno formula, be virtue of several identities for the Bell polynomials of the second kind, with help of two combinatorial identities, by means of the (logarithmically) complete monotonicity of…
We prove an inverse relation and a family of convolution formulas involving partial Bell polynomials. Known and some presumably new combinatorial identities of convolution type are discussed. Our approach relies on an interesting…
We offer a solution to a functional equation using properties of the Mellin transform. A new criteria for the Riemann Hypothesis is offered as an application of our main result, through a functional relationship with the Riemann xi…
Results of research of possibility of transformation of a difference equation into a system of the first-order difference equation are presented. In contrast to the method used previously, an unknown grid function is split into two new…
Using a special case of the Efros theorem which was derived by Wlodarski, and operational calculus, it was possible to derive many infinite integrals, finite integrals and integral identities for the function represented by the inverse…
In this article, a class of analytic functions is investigated and their some properties are established. Several recurrence relations and various classes of bilinear and bilateral generating functions for these analytic functions are also…
This is an introduction to calculus, and its applications to basic questions from physics. We first discuss the theory of functions $f:\mathbb R\to\mathbb R$, with the notion of continuity, and the construction of the derivative $f'(x)$ and…
A natural consequence of the fractional calculus is its extension to a matrix order of differentiation and integration. A matrix-order derivative definition and a matrix-order integration arise from the generalization of the gamma function…
We consider invariant hyperfunctions associated to automorphic forms on the upper half plane. We give two interpretations of the period function of Maass forms introduced by Lewis. The first interpretation shows that the period function…