Flows with limited intersection of worldlines [PDF]
arXiv, 2014 In this paper we define a flow with limited intersection of its worldlines and we construct and solve functional equations for such flow using a special kind of set embedding. For examples we use particular cases studied in the past by different authors. The connection to higher order ordinary differential equations is emphasized.
arxiv
Hyers--Ulam Stability for Discrete Time Scale with Two Step Sizes [PDF]
arXiv, 2018 We clarify the Hyers--Ulam stability (HUS) of certain first-order linear constant coefficient dynamic equations on time scales, in the case of a specific time scale with two alternating step sizes, where the exponential function changes sign. In particular, in the case of HUS, we discuss the HUS constant, and whether a minimal constant can be found.
arxiv
On different types of stability for linear delay dynamic equations [PDF]
Z. Anal. Anwend. 36 (2017), no. 3, 343-375, 2019 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 given to show applicability and sharpness of the new results.
arxiv
Unifying discrete and continuous Weyl-Titchmarsh theory via a class of linear Hamiltonian systems on Sturmian time scales [PDF]
, 2010 In this study, we are concerned with introducing Weyl-Titchmarsh theory for a class of dynamic linear Hamiltonian nabla systems over a half-line on Sturmian time scales.
Anderson, Douglas R.
core
A generalized Gronwall Inequality for Caputo Fractional Dynamic delta operator [PDF]
arXiv, 2019 In this paper we obtain generalized Gronwall type inequality using Caputo Fractional delta operator. Also we have obtained the existence of solution of Cauchy's Type problem on fractional dynamic equations using dynamic delta operator. Applying the obtained inequality we study the properties of solution on fractional dynamic equations.
arxiv
On the quasi-steady-state approximation in an open Michaelis-Menten reaction mechanism. [PDF]
AIMS Math, 2021 Eilertsen J +3 more
europepmc +1 more source
Polytropic Dynamical Systems with Time Singularity [PDF]
In this paper we consider a class of second order singular homogeneous differential equations called the Lane-Emden-type with time singularity in the drift coefficient. Lane-Emden equations are singular initial value problems that model phenomena in astrophysics such as stellar structure and are governed by polytropics with applications in isothermal ...
arxiv +1 more source
Qualitative analysis of dynamic equations on time scales
, 2018 In this article, we establish the Picard-Lindelof theorem and approximating results for dynamic equations on time scale. We present a simple proof for the existence and uniqueness of the solution.
Abbas, Syed
core +1 more source
A Survey of Function Analysis and Applied Dynamic Equations on Hybrid Time Scales. [PDF]
Entropy (Basel), 2021 Wang C, Agarwal RP.
europepmc +1 more source
New definitions of exponential, hyperbolic and trigonometric functions on time scales
, 2010 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.
Cieslinski, Jan L.
core