Related papers: On the Weber integral equation and solution to the…

We use the Laplace transform and the Gamma function to introduce a new integral transform and name it the Laplace-type transform possessing the property of mapping a function to a functional sequence, which cannot be achieved by the Laplace…

In this paper we consider the problem of estimation of oscillatory integrals with Mittag-Leffler functions in two variables. The generalisation is that we replace the exponential function with the Mittag-Leffler-type function, to study…

We discuss the solvability of a fairly general class of systems of perturbed Hammerstein integral equations with functional terms that depend on several parameters. The nonlinearities and the functionals are allowed to depend on the…

The classical Lebedev index transform (1967), involving squares and products of the Legendre functions is generalized on the associated Legendre functions of an arbitrary order. Mapping properties are investigated in the Lebesgue spaces.…

Based on a Problem and its solution published on the pages of SIAM Review, we give an interesting integral representation for the Lambert $W$ function in this short note. In particular, our result yields a new integral representation for…

In the first part of the paper, some extensions of the classical Dynkin-Specht-Wever lemma are developed. In the second part, we extend Burgunder's splitting construction, and relate back to the Kashiwara-Vergne problem.

This paper deals with the evaluation of some definite Euler-type integrals in terms of the Wright hypergeometric function. We obtain a theorem on the Wright hypergeometric function and then use this theorem to evaluate some definite…

The Lamb-Bateman integral equation was introduced to study the solitary wave diffraction and its solution was written in terms of an integral transform. We prove that it is essentially the Abel integral equation and its solution can be…

This paper introduces two forms of modular inverses and proves their reciprocity formulas respectively. These formulas are then applied to formulate new and generalized algorithm for computing these modular inverses. The same algorithm is…

We generalize some classical results for the Schlesinger system of partial differential equations and give the explicit form of its solution, associated with rational matrix functions in general position.

We establish a relative Bertini type theorem for multiplier ideal sheaves. Then we prove a relative version of the Koll\'ar--Nadel type vanishing theorem as an application.

Burgers' equation with fixed Dirichlet boundary conditions is considered on generic bounded intervals. By using the Hopf-Cole transformation and the exact operational solution recently established for linear reaction-diffusion equations…

In this paper, the author establishes some Hadamard-type and Bullen-type inequalities for Lipschitzian functions via Riemann Liouville fractional integral. These results have some relationships with [K.-L. Tseng, S.-R. Hwang and K.-C. Hsu,…

We give a functional equation for the refined Herglotz-Zagier function. It is analogous to a result in the theory of modular forms.

Inverse problem to recover the skew-self-adjoint Dirac-type system from the generalized Weyl matrix function is treated in the paper. Sufficient conditions under which the unique solution of the inverse problem exists, are formulated in…

In this work, we introduce a novel numerical method for solving initial value problems associated with a given differential. Our approach utilizes a spline approximation of the theoretical solution alongside the integral formulation of the…

We deal with the Cauchy problem for the space-time fractional diffusion-wave equation, which is obtained from the standard diffusion equation by replacing the second-order space derivative with a Riesz-Feller derivative of order alpha in…

In this paper, we bring a complete solution to the Ovals problem, as formulated in [3] and [24].

In this paper we have chosen to work with two different approaches to solving the inverse problem of the calculus of variation. The first approach is based on an integral representation of the Lagrangian function that uses the first…

In the series of papers [1-4], the inverse problem of the Birkhoff-Gustavson normalization was posed and studied. To solve the inverse problem, the symbolic-computing program named ANFER (Algorithm of Normal Form Expansion and Restoration)…