Related papers: On a class of functional difference equations: exp…

Consider non-linear time-fractional stochastic heat type equations of the following type, $$\partial^\beta_tu_t(x)=-\nu(-\Delta)^{\alpha/2} u_t(x)+I^{1-\beta}_t[\lambda \sigma(u)\stackrel{\cdot}{F}(t,x)]$$ in $(d+1)$ dimensions, where…

Take complex numbers $a_j,b_j$, $(j=0,1,2)$ such that $c\neq0$ and {\rm rank} ( {ccc} a_{0} & a_{1} & a_{2} b_{0} & b_{1} & b_{2} )=2. We show that if the following functional equation of Fermat type…

For $\gamma\in\IC$ such that $|\gamma|<\pi/2$ and $0\leq\beta<1$, let ${\mathcal P}_{\gamma,\beta} $ denote the class of all analytic functions $P$ in the unit disk $\mathbb{D}$ with $P(0)=1$ and $$ {\rm Re\,} \left…

We present several formulae for the large-$t$ asymptotics of the modified Hurwitz zeta function $\zeta_1(x,s),x>0,s=\sigma+it,0<\sigma\leq1,t>0,$ which are valid to all orders. In the case of $x=0$, these formulae reduce to the asymptotic…

We study the parameters range for the fixed point of a class of complex dynamics with the rational fractional function as $R_{n,a,c}(z)=z^n+\frac{a}{z^n}+c$, where $n=1,2,3,4$ is specified, $a$ and $c$ are two complex parameters. The…

For R(z, w) rational with complex coefficients, of degree at least 2 in w, we show that the number of rational functions f(z) solving the difference equation f(z+1)=R(z, f(z)) is finite and bounded just in terms of the degrees of R in the…

In this paper, we study the asymptotic behavior of a semi-linear slow-fast stochastic partial differential equation with singular coefficients. Using the Poisson equation in Hilbert space, we first establish the strong convergence in the…

In this manuscript, we consider the Riemann zeta function $\zeta$, defined through the Abel summation formula. We present a simple analytical method based on a complex differential equation. The aim is to propose a new analytical approach,…

A complex function $f(z)$ is called a Herglotz-Nevanlinna function if it is holomorphic in the upper half-plane ${\mathbb C}_+$ and maps ${\mathbb C}_+$ into itself. By a maximum principle a Herglotz-Nevanlinna function which takes a real…

We consider a rational system of first order difference equations in the plane with four parameters such that all fractions have a common denominator. We study, for the different values of the parameters, the global and local properties of…

In the present series of papers, we study the behavior of the r-fold zeta-function of Euler-Zagier type with identical arguments on the real line. In this first part, we consider the behavior on the interval [0,1]. Our basic tool is an…

A Master equation has been previously obtained which allows the analytic integration of a fairly large family of functions provided that they possess simple properties. Here, the properties of this Master equation are explored, by extending…

For a subshift $(X, \sigma_X)$ and a subadditive sequence $\mathcal{F}=\{\log f_n\}_{n=1}^{\infty}$ on $X$, we study equivalent conditions for the existence of $h\in C(X)$ such that $\lim_{n\rightarrow\infty}(1/{n})\int \log f_n d \mu=\int…

The well-known algorithm for summing of divergent series is based on the Borel transformation in combination with the conformal mapping (Le Guillou and Zinn-Justin, 1977). Modification of this algorithm allows to determine a strong coupling…

Asymptotic relations between zeta functions (such as, $\zeta(s),\,\beta(s)$, and other Dirichlet $L$-functions) and interpolation differences of functions like $\vert y\vert^s$ and their interpolating entire functions of exponential type…

The aim of the paper is to investigate the solutions of special inhomogeneous linear functional equations by using spectral analysis in a translation invariant closed linear subspace of additive/multiadditive functions containing the…

Taking up a variational viewpoint, we present some nonlocal-to-local asymptotic results for various kinds of integral functionals. The content of the thesis comprises the contributions first appeared in some research papers in collaboration…

We consider the asymptotic expansion of the Wright function \[W_{\lambda,\mu}(z)=\sum_{n=0}^\infty\frac{z^n}{n! \Gamma(\lambda n+\mu)}\qquad (\lambda>-1)\] for large (positive and negative) variable and large parameter $\mu$. The analysis…

In this paper we obtain the precise description of the asymptotic behavior of the solution $u$ of $$ \partial_t u+(-\Delta)^{\frac{\theta}{2}}u=0\quad\mbox{in}\quad{\bf R}^N\times(0,\infty), \qquad u(x,0)=\varphi(x)\quad\mbox{in}\quad{\bf…

In this article we study the asymptotic behavior of solutions of some fractional differential equations. We prove convergence to power type functions under some assumptions on the nonlinearities. Our results extend and generalize some…