Related papers: Certain triple q-integral equations involving thir…
Fractional vector calculus is discussed in the spherical coordinate framework. A variation of the Legendre equation and fractional Bessel equation are solved by series expansion and numerically. Finally, we generalize the hypergeometric…
A representation for the kernel of the transmutation operator relating the perturbed Bessel equation with the unperturbed one is obtained in the form of a functional series with coefficients calculated by a recurrent integration procedure.…
We introduce an efficient algorithm for computing fractional integrals and derivatives and apply it for solving problems of the calculus of variations of fractional order. The proposed approximations are particularly useful for solving…
We give a unified interpretation of confluences, contiguity relations and Katz's middle convolutions for linear ordinary differential equations with polynomial coefficients and their generalization to partial differential equations. The…
In this paper we study fractional powers of the Bessel differential operator defined on a semiaxis. Some important properties of such fractional powers of the Bessel differential operator are proved. They include connections with Legendre…
Decay rates for the sequence of eigenvalues of positive and compact integral operators has been largely investigated for a long time in the literature. In this paper, the focus will be on positive integral operators acting on square…
Firstly, we construct kernels of integral relations among solutions of the confluent Heun equation (CHE) and its limit, the reduced CHE (RCHE). In both cases we generate additional kernels by systematically applying substitutions of…
This paper aims to study the q-analogue of the Sturm Liouville problem and to give an asymptotic behaviour at infinity for its solution '. Additionally, we establish an asymptotic expansion of the q-Bessel function $j_\alpha$ for $\alpha…
We introduce an efficient variational hybrid quantum-classical algorithm designed for solving Caputo time-fractional partial differential equations. Our method employs an iterable cost function incorporating a linear combination of overlap…
We introduce an algebraic theory of integration on quantum planes and other braided spaces. In the one dimensional case we obtain a novel picture of the Jackson $q$-integral as indefinite integration on the braided group of functions in one…
We investigate solutions for a particular class of linear equations in dendriform algebras. Motivations as well as several applications are provided. The latter follow naturally from the intimate link between dendriform algebras and…
Many possible definitions have been proposed for fractional derivatives and integrals, starting from the classical Riemann-Liouville formula and its generalisations and modifying it by replacing the power function kernel with other kernel…
Several kernel-based methods for the numerical solution of fractional differential equations have been developed in the recent past; however, these techniques exclusively relied on the use of radial basis function approximations. In the…
In this paper we present a new boundary integral equation formulation for the solution of the elastostatic traction boundary value problem in two and three dimensions. The approach relies on the introduction of new layer potentials, called…
We provide an explicit expression for the first order $q$-difference system for the Jackson integral of symmetric Selberg type. The $q$-difference system gives a generalization of $q$-analog of contiguous relations for the Gauss…
The aim of this note is to provide a fractional integration theorem in the framework of Laguerre expansions. The method of proof consists of establishing an asymptotic estimate for the involved kernel and then applying a method of Hedberg…
We discuss the inequalities for $q$-integrals because of the fact that the inequalities can be very useful in the future mathematical research. Since $q$-integral of a function over an interval $[a,b]$ is defined by the difference of two…
The inverse quantum scattering problem for the perturbed Bessel equation is considered. A direct and practical method for solving the problem is proposed. It allows one to reduce the inverse problem to a system of linear algebraic…
The kernel polynomial method allows to sample overall spectral properties of a quantum system, while sparse diagonalization provides accurate information about a few important states. We present a method combining these two approaches…
We study a critical case of Coagulation-Fragmentation equations with multiplicative coagulation kernel and constant fragmentation kernel. Our method is based on the study of viscosity solutions to a new singular Hamilton-Jacobi equation,…