相关论文: A Study of Diamond-alpha dynamic equations on regu…
We introduce a nabla, a delta, and a symmetric fractional calculus on arbitrary nonempty closed subsets of the real numbers. These fractional calculi provide a study of differentiation and integration of noninteger order on discrete,…
A general solution for a second-order linear constant coefficient dynamic equation with polynomial forcing on time scales is given.
Simple form scalar differential equation with delay and nonlinear negative periodic feedback is considered. The existence of several types of slowly oscillating periodic solutions is shown with the same and double periods of the feedback…
We discuss asymptotic solutions of the kinematic $\alpha\omega$-dynamo in a thin disc (slab). Focusing upon the strong dynamo regime, in which the dynamo number $D$ satisfies $|D|\gg1$, we resolve uncertainties in the earlier treatments and…
A conformable time-scale fractional calculus of order $\alpha \in ]0,1]$ is introduced. The basic tools for fractional differentiation and fractional integration are then developed. The Hilger time-scale calculus is obtained as a particular…
The linear nonhomogeneous fractional difference system with constant coefficients is introduced. An explicit solution to the system is acquired by proposing a newly discrete retarded perturbation of the nabla Mittag-Leffer-type function…
We provide explicit conditions for uniform stability, global asymptotic stability and uniform exponential stability for dynamic equations with a single delay and a nonnegative coefficient. Some examples on nonstandard time scales are also…
We develop techniques at the interface between differential algebra and model theory to study the following problems of exponential algebraicity: Does a given algebraic differential equation admits an exponentially algebraic solution, that…
We consider a system of differential equations and obtain its solutions with exponential asymptotics and analyticity with respect to the spectral parameter. Solutions of such type have importance in studying spectral properties of…
In this article we consider a special type of degenerate elliptic partial differential equations of second order in convex domains that satisfy the interior sphere condition. We show that any positive viscosity solution $u$ of $-|\nabla…
We propose two new definitions of the exponential function on time scales. The first definition is based on the Cayley transformation while the second one is a natural extension of exact discretizations. Our eponential functions map the…
In this paper, we reformulate certain nabla fractional difference equations which had been investigated by other researchers. The previous results seem to be incomplete. By using Contraction Mapping Theorem, we establish conditions under…
A steady scalar convection-diffusion problem has been studied for one and two dimensional cases. The major problem of unrealistic oscillations of the convection dominated problems is relaxed thanks to the wide range of the elements FEMLAB…
An exponentially convergent numerical method for solving a differential equation with a right-hand fractional Riemann-Liouville time-derivative and an unbounded operator coefficient in Banach space is proposed and analysed for a…
In this paper, we delve into the fascinating realm of fractal calculus applied to fractal sets and fractal curves. Our study includes an exploration of the method analogues of the separable method and the integrating factor technique for…
In this paper, we introduce the nabla fractional derivative and fractional integral on time scales in the Riemann-Liouville sense. We also introduce the nabla fractional derivative in Gr\"unwald-Letnikov sense. Some of the basic properties…
We prove a necessary optimality condition of Euler-Lagrange type for variational problems on time scales involving nabla derivatives of higher-order. The proof is done using a new and more general fundamental lemma of the calculus of…
We obtain explicit criteria for both exponential ergodicity and strong ergodicity for one-dimensional time-changed symmetric stable processes with $\alpha\in(1,2)$. Explicit lower bounds for ergodic convergence rates are given.
This paper is devoted to the analysis of the problem of stabilization of fractional (in time) partial differential equations. We consider the following equation $$ \partial^{\alpha,\eta}_{t} u(t)=\mathcal{A}u(t)-\frac{\eta}{\Gamma…
Analytic solutions of the mean-field induction equation predict a nonoscillatory dynamo for homogeneous helical turbulence or constant alpha effect in unbounded or periodic domains. Oscillatory dynamos are generally thought impossible for…