Related papers: Differential Equations with a Difference Quotient
Partial differential equations with discrete (concentrated) state-dependent delays in the space of continuous functions are investigated. In general, the corresponding initial value problem is not well posed, so we find an additional…
The work considers a system of fractional order partial differential equations. The existence and uniqueness theorems for the classical solution of initial-boundary value problems are proved in two cases: 1) the right-hand side of the…
A nonlinear partial differential equation is a nonlinear relationship between an unknown function and how it changes due to two or more input variables. A numerical method reduces such an equation to arithmetic for quick visualization, but…
The dynamics of physical theories is usually described by differential equations. Difference equations then appear mainly as an approximation which can be used for a numerical analysis. As such, they have to fulfill certain conditions to…
We study some classes of semi-linear differential equations including both well-posed and ill-posed cases that can generate cocycles (or cocycle correspondences with generating cocycles). Under exponential dichotomy condition with other…
Differential equations with constant and variable coefficients over octonions are investigated. It is found that different types of differential equations over octonions can be resolved. For this purpose non-commutative line integration is…
Numerical solving differential equations with fractional derivatives requires elimination of the singularity which is inherent in the standard definition of fractional derivatives. The method of integration by parts to eliminate this…
We present a new approach to solving polynomial ordinary differential equations by transforming them to linear functional equations and then solving the linear functional equations. We will focus most of our attention upon the first-order…
We develop an operator-theoretical method for the analysis on well posedness of partial differential equations that can be modeled in the form \begin{equation*} \left\{ \begin{array}{rll} \Delta^{\alpha} u(n) &= Au(n+2) + f(n,u(n)), \quad n…
Let $f(t,x),M(t,x)\in C([0,1]^2)$ with $M(t,x)>0$. We consider differential equations of the form \[ \frac{\partial f}{\partial t}(t,x)=\frac{M(t,x)f(t,x)-M(t,0)f(t,0)}{x},\quad x>0. \] For a fixed positive weight $M$, we ask whether the…
Given the solution $f$ of the sequential fractional differential equation $_{a}D_{t}^{\alpha}(_{a}D_{t}^{\alpha}f)+P(t)f=0$, $t\in[b,c]$, where $-\infty<a<b<c<+\infty$, $\alpha\in({1/2},1)$ and $P:[a,+\infty)\to[0,P_{\infty}]$,…
When considering fractional diffusion equation as model equation in analyzing anomalous diffusion processes, some important parameters in the model, for example, the orders of the fractional derivative or the source term, are often unknown,…
This work deals with the existence of an almost periodic solution for certain kind of differential equations with generalized piecewise constant argument, almost periodic coefficients which are seen as a perturbation of a linear equation of…
Assume that $n$ is a positive integer, $p_{j}$ ($j=1,2, \cdots, 6)$ are polynomials, $p$ is an irreducible polynomial, and $f$ is an entire function on $\mathbb{C}^{n}.$ Let $ L(f)=\sum_{j=1}^s q_{t_j}f_{z_{t_j}}$ and…
This work is dedicated to the study of a mixed-type partial differential equation involving a Caputo fractional derivative in the time domain $t > 0$ and a classical parabolic equation in the domain $t < 0$, along with Dezin-type non-local…
We consider the uniqueness of solutions of ordinary differential equations where the coefficients may have singularities. We derive upper bounds on the the order of singularities of the coefficients and provide examples to illustrate the…
In this note we prove some new results about the application of Wright functions of the first kind to solve fractional differential equations with variable coefficients. Then, we consider some applications of these results in order to…
This paper reviews a class of univariate piecewise polynomial functions known as discrete splines, which share properties analogous to the better-known class of spline functions, but where continuity in derivatives is replaced by (a…
A boundary value problem associated to the difference equation with advanced argument \begin{equation} \label{*}\Delta\bigl (a_{n}\Phi(\Delta x_{n})\bigr)+b_{n}\Phi(x_{n+p} )=0,\ \ n\geq1 \tag{$*$} \end{equation} is presented, where…
We study existence and uniqueness of bounded solutions to a fractional sublinear elliptic equation with a variable coefficient, in the whole space. Existence is investigated in connection to a certain fractional linear equation, whereas the…