Related papers: Differential Equations with a Difference Quotient
This paper deals with fractional differential equations, with dependence on a Caputo fractional derivative of real order. The goal is to show, based on concrete examples and experimental data from several experiments, that fractional…
Finite differences have been widely used in mathematical theory as well as in scientific and engineering computations. These concepts are constantly mentioned in calculus. Most frequently-used difference formulas provide excellent…
This is the continuation of previous article. For subspaces $M^n(t)$ and $M^{n-m}(t)$ which are invariant manifolds of the differential equation under consideration we build a change of variables which splits this equation into a system of…
We propose a new method for solution of the integrability problem for evolutionary differential-difference equations of arbitrary order. It enables us to produce necessary integrability conditions, to determine whether a given equation is…
Fractional difference equations provide a flexible mathematical framework for modeling complex systems with memory, hereditary, and non-local effects. In this work, we study the stability of higher-order two-term fractional linear…
The aim of this work is to study the existence of a periodic solutions of third order differential equations $z'''(t) = Az(t) + f(t)$ with the periodic condition $x(0) = x(2\pi), x'(0) = x'(2\pi)$ and $x''(0) = x''(2\pi)$. Our approach is…
The uniqueness problems on transcendental meromorphic or entire functions sharing at least two values with their derivatives or linear differential polynomials have been studied and many results have been obtained. In this paper, we study a…
We consider stochastic PDEs \[dY_t = L(Y_t)\, dt + A(Y_t).\, dB_t, t > 0\] and associated PDEs \[du_t = L u_t\, dt, t > 0\] with regular initial conditions. Here, $L$ and $A$ are certain partial differential operators involving…
We study existence, uniqueness and regularity of solutions for ordinary differential equations with infinitely many derivatives such as (linearized versions of) nonlocal field equations of motion appearing in particle physics, nonlocal…
It is classical that univariate algebraic functions satisfy linear differential equations with polynomial coefficients. Linear recurrences follow for the coefficients of their power series expansions. We show that the linear differential…
We explore partitions that lie in the intersection of several sets of classical interest: partitions with parts indivisible by $m$, appearing fewer than $m$ times, or differing by less than $m$. We find results on their behavior and…
We propose a new notion of Partial Inertial Manifold to study the long-time asymptotic behavior of dissipative differential equations. As shown on an example, such manifolds may exist in the cases when the classical Inertial manifold does…
In this paper, we introduce a new method for calculating fractional integrals and differentials. The method involves an equation that we have obtained from infinite applied integration by parts. The equation works for special class of…
In this paper, we study about existence and non-existence of finite order transcendental entire solutions of the certain non-linear differential-difference equations. We also study about conjectures posed by Rong et al. and Chen et al.
A class of first order linear impulsive differential equation with continuous and piecewise constant arguments is studied. Sufficient conditions for the oscillation of the solutions are obtained.
In this paper we investigate the asymptotic distribution of the zeros of polynomials $P_{n}(x)$ satisfying a first order differential-difference equation. We give several examples of orthogonal and non-orthogonal families.
We consider delay differential equations with a polynomially distributed delay. We derive an equivalent system of delay differential equations, which includes just two discrete delays. The stability of the equivalent system and its…
In this paper, we consider a class of nonlinear fractional differential equations involving Hilfer derivative with boundary conditions. First, we obtain an equivalent integral for the given boundary value problem in weighted space of…
In this article, we study the existence and multiplicity of solutions of the following $(p,q)$-Laplace equation with singular nonlinearity: \begin{equation*} \left\{\begin{array}{rllll} -\Delta_{p}u-\ba\Delta_{q}u & = \la u^{-\de}+ u^{r-1},…
The aim of this paper is a quantitative analysis of the solution set of a system of polynomial nonlinear differential equations, both in the ordinary and partial case. Therefore, we introduce the differential counting polynomial, a common…