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We study the properties of the set where a generalized function of bounded variation has infinite approximate limit, highlighting in this way the main geometric difference with functions of bounded variation. To this aim we prove a new…

We combine the method of exchangeable pairs with Stein's method for functional approximation. As a result, we give a general linearity condition under which an abstract Gaussian approximation theorem for stochastic processes holds. We apply…

We present a general framework for the rigorous numerical analysis of time-fractional nonlinear parabolic partial differential equations, with a fractional derivative of order $\alpha\in(0,1)$ in time. The framework relies on three…

We prove existence and uniqueness of the solution for a class of mixed fractional stochastic differential equations with discontinuous drift driven by both standard and fractional Brownian motion. Additionally, we establish a generalized…

We prove a general theorem to bound the total variation distance between the distribution of an integer valued random variable of interest and an appropriate discretized normal distribution. We apply the theorem to 2-runs in a sequence of…

The authors previous derivation of a variational principle from the total work functional, as a generalization of the first variation of an action functional, is extended by deriving a corresponding generalization of the Hamiltonian…

In this article, we discuss the basic ideas of a general procedure to adapt the Stein-Chen method to bound the distance between conditional distributions. From an integration-by-parts formula (IBPF), we derive a Stein operator whose…

The nabla fractional derivative, which was introduced by Gogoi et.al., generalized the ordinary derivative with non-integer order, and unifies the continuous and discrete analysis using backward operator. In this study, we proposed a…

The calculus of variations for lagrangians which are not functions on the tangent bundle, but sections certain affine bundles is developed. We follow a general approach to variational principles which admits boundary terms of variations.

After reviewing the problematic behavior of some previously suggested finite interval spatial operators of the symmetric Riesz type, we create a wish list leading toward a new spatial operator suitable to use in the space-time fractional…

We study random one-Lipschitz integer functions $f$ on the vertices of a finite connected graph, sampled according to the weight $W(f) = \prod_{\langle v, w \rangle \in E} \mathbf{c}^{ \mathbb{I} \{ f(v) = f(w) \} }$ where $\mathbf{c} \geq…

This paper is concerned with the differential sensitivity analysis of variational inequalities in Banach spaces whose solution operators satisfy a generalized Lipschitz condition. We prove a sufficient criterion for the directional…

In this paper, using the tools from the lineability theory, we distinguish certain subsets of $p$-adic differentiable functions. Specifically, we show that the following sets of functions are large enough to contain an infinite dimensional…

It has recently been shown that complete Bernstein functions of the Laplace operator map the Dirichlet boundary condition of a related elliptic PDE to the Neumann boundary condition. The importance of this mapping consists in being able to…

The separation dimension of a graph $G$, written $\pi(G)$, is the minimum number of linear orderings of $V(G)$ such that every two nonincident edges are "separated" in some ordering, meaning that both endpoints of one edge appear before…

In this paper, we consider some aspects of the numerical analysis of the mathematical model of fractional Duffing with a derivative of variable fractional order of the Riemann-Liouville type. Using numerical methods: an explicit…

We prove global Lipschitz regularity for a wide class of convex variational integrals among all functions in $W^{1,1}$ with prescribed (sufficiently regular) boundary values, which are not assumed to satisfy any geometrical constraint (as…

We consider some possible approaches to the fractional-order generalization of definition of variation (functional) derivative. Some problems of formulation of a fractional-order variational derivative are discussed. To give a consistent…

We establish a general structure theorem for the singular part of ${\mathscr A}$-free Radon measures, where ${\mathscr A}$ is a linear PDE operator. By applying the theorem to suitably chosen differential operators ${\mathscr A}$, we obtain…

We consider a sequence of additive functionals {\phi_n}, set on a sequence of Markov chains {X_n} that weakly converges to a Markov process X. We give sufficient condition for such a sequence to converge in distribution, formulated in terms…