Related papers: Fr\'echet differentiability in Fr\'echet spaces, a…
We study monotone skew-product semiflows generated by families of nonautonomous neutral functional differential equations with infinite delay and stable D-operator, when the exponential ordering is considered. Under adequate hypotheses of…
For fractional derivatives and time-fractional differential equations, we construct a framework on the basis of the operator theory in fractional Sobolev spaces. Our framework provides a feasible extension of the classical Caputo and the…
This paper investigates the stability of different regions in the $(k,\gamma)$-plane for a class of fractional delay differential equations given by \begin{equation} D^{\alpha} x(t) = -\gamma x(t) + g\big(x(t - \tau_1)\big) - e^{-\gamma…
This article provides an exposition of recent methodologies for nonparametric analysis of digital observations on images and other non-Euclidean objects. Fr\'echet means of distributions on metric spaces, such as manifolds and stratified…
We introduce fractional weighted Sobolev spaces with degenerate weights. For these spaces we provide embeddings and Poincar\'e inequalities. When the order of fractional differentiability goes to $0$ or $1$, we recover the weighted Lebesgue…
Using the method of similar operators we study an even order differential operator with periodic, semiperiodic, and Dirichlet boundary conditions. We obtain asymptotic formulas for eigenvalues of this operator and estimates for its spectral…
This work establishes a comprehensive analytical framework for studying implicit fractional differential systems with distributed memory and time delays. We develop novel fractional integral inequalities of Gr\"onwall--Wendroff type that…
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…
This article introduces a novel approach for broken-FEEC (Finite Element Exterior Calculus), extending its application to locally refined spline spaces with non-matching interfaces. Traditional broken-FEEC allows for discontinuous…
A characteristic matrix function captures the spectral information of a bounded linear operator in a matrix-valued function. In this article, we consider a delay differential equation with one discrete time delay and assume this equation is…
This paper develops the necessary ingredients for the variational approach of initial boundary-value problems of parabolic partial differential equations on a fixed spatial domain containing evolving subdomains. In particular, we introduce…
We show the continuous dependence of solutions of linear nonautonomous second order parabolic partial differential equations (PDEs) with bounded delay on coefficients and delay. The assumptions are very weak: only convergence in the weak-*…
In this paper we lay the foundations for the Morse theoretical study of strongly indefinite functionals on Banach manifolds by developing the local theory for a specific model class that captures several key analytical features also arising…
Differential forms on the Fr\'echet manifold F(S,M) of smooth functions on a compact k-dimensional manifold S can be obtained in a natural way from pairs of differential forms on M and S by the hat pairing. Special cases are the…
We develop mathematical framework and computational tools for calculating frequency responses of linear time-invariant PDEs in which an independent spatial variable belongs to a compact interval. In conventional studies this computation is…
We prove convergence of piecewise polynomial collocation methods applied to periodic boundary value problems for functional differential equations with state-dependent delays. The state dependence of the delays leads to nonlinearities that…
We study variational problems for integral invariants, which are defined as integrations of invariant functions of the second fundamental form, of a smooth map between pseudo-Riemannian manifolds. We derive the first variational formulae…
We identify the stochastic processes associated with one-sided fractional partial differential equations on a bounded domain with various boundary conditions. This is essential for modelling using spatial fractional derivatives. We show…
We show in this note that the Ito-Lyons solution map associated to a rough differential equation is Frechet differentiable when understood as a map between some Banach spaces of controlled paths. This regularity result provides an…
We apply the topology of convergence on compact sets to define unpredictable functions [5, 6]. The topology is metrizable and easy for applications with integral operators. To demonstrate the effectiveness of the approach, the existence and…