Abstract In this article, we study the asymptotic behavior of even-order neutral delay differential equation ( a ⋅ u + ρ ∘ τ stretchy="false">) n −</m:m...

We develop the general formalism for the study of neutrino propagation in presence of stochastic media. This formalism allows the systematic derivation of evolution equations for averaged quantities as survival probabilities and higher order distribution moments. The formalism applies equally to any finite dimensional Schroedinger equation in presence of a stochastic external field. New integro...

Modeling continuous dynamical systems from discretely sampled observations is a fundamental problem in data science. Often, such dynamics are the result of non-local processes that present an integral over time. As such, these modeled with Integro-Differential Equations (IDEs); generalizations differential equations comprise both and component. For example, brain not accurately by since their b...

This paper concerns the dissipativity and stability of the Caputo nonlinear fractional functional differential equations (F-FDEs) with order 0 < α < 1. The fractional generalization of the Halanay-type inequality is proposed, which plays a central role in studies of stability and dissipativity of F-FDEs. Then the dissipativity and the absorbing set are derived under almost the same assumptions ...

We review some regularity results for integro-differential equations, focusing on Hölder estimates for equations with rough kernels and their applications. We show that if we take advantage of the integral form of the equation, we can obtain simpler proofs than for second order equations. For the equations considered here, the Harnack inequality may not hold. Mathematics Subject Classification ...