Related papers: Computing solutions of the modified Bessel differe…
We develop a general technique for computing functional integrals with fixed area and boundary length constraints. The correct quantum dimensions for the vertex functions are recovered by properly regularizing the Green function. Explicit…
Although being powerful, the differential transform method yet suffers from a drawback which is how to compute the differential transform of nonlinear non-autonomous functions that can limit its applicability. In order to overcome this…
This paper is concerned with the study of diagonal Diophantine inequalities of fractional degree $ \theta ,$ where $ \theta >2$ is real and non-integral. For fixed non-zero real numbers $ \lambda_i $ not all of the same sign we write…
We propose a method to numerically compute fractional derivatives (or the fractional Laplacian) on the whole real line via Riesz fractional integrals. The compactified real line is divided into a number of intervals, thus amounting to a…
Linear second-order ordinary differential equations of the form $d^{2}w/dz^{2}=\{u^{2}f(a,z)$ $+g(z)\}w$ are studied for large values of the real parameter $u$, where $z$ ranges over a bounded or unbounded complex domain $Z$, and $a_{0} \le…
Mathematical models are sometime given as functions of independent input variables and equations or inequations connecting the input variables. A probabilistic characterization of such models results in treating them as functions with…
Derivatives with respect to the parameters of the integral Mittag-Leffler function and the integral Wright function, recently introduced by us, are calculated. These derivatives can be expressed in the form of infinite sums of quotients of…
In this paper we consider a boundary value problem for fully fourth order nonlinear functional differential equation which contains all lower derivatives of proportional delay arguments. By the reduction of the problem to operator equation…
In this paper, we first deal with the general fractional derivatives of arbitrary order defined in the Riemann-Liouville sense. In particular, we deduce an explicit form of their null space and prove the second fundamental theorem of…
We are interested in classical and logarithmic imaginary classes of abelian number fields in connection with Iwasawa theory. For any given odd prime ${\ell}$ and any imaginary abelian number field K, we compute the isotypic components of…
It is well known that second order linear ordinary differential equations with slowly varying coefficients admit slowly varying phase functions. This observation is the basis of the Liouville-Green method and many other techniques for the…
A variety of problems emerged investigating electronic circuits, computer devices and cellular automata motivated a number of attempts to create a differential and integral calculus for Boolean functions. In the present article, we extend…
The main objective of this paper is to study the existence of solutions to some basic fractional difference equations. The tools employed are Krasnosel'skii fixed point theorem which guarantee at least two positive solutions.
Integral representations are derived for the parabolic cylinder functions $U(a,x)$, $V(a,x)$ and $W(a,x)$ and their derivatives. The new integrals will be used in numerical algorithms based on quadrature. They follow from contour integrals…
Coefficient inverse problems related to identifying the right-hand side of an equation with use of additional information is of interest among inverse problems for partial differential equations. When considering non-stationary problems,…
In this paper, we prove an exponential integral formula for the Fourier transform of Bessel functions over complex numbers, along with a radial exponential integral formula. The former will enable us to develop the complex spectral theory…
New index transforms, involving the square of Bessel functions of the first kind as the kernel are considered. Mapping properties such as the boundedness and invertibility are investigated for these operators in the Lebesgue spaces.…
Let A be an arbitrary countable set of reals, for example A=Q. Let g be an arbitrary mapping from A into the positive reals, for example g(a)=2^a. We show how a strictly increasing real function f can be constructed such that f'(x)=g(x) for…
Discrete analogs of the index transforms with squares of Bessel functions of the first and second kind $J_\nu(z),\ Y_\nu(z)$ are introduced and investigated. The corresponding inversion theorems for suitable classes of functions and…
A formula for the Hurwitz zeta function at the positive integers $k$, $\zeta(k,b)$, is created by solving the real and the imaginary parts separately and then combining them. A few different formulae for the Hurwitz zeta function are known…