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Difference schemes for the time-fractional diffusion equation with variable coefficients and nonlocal boundary conditions containing real parameters $\alpha$ and $\beta$ are considered. By the method of energy inequalities, for the solution…

In this paper, stability and synchronization of a Caputo fractional BAM neural network system of high-order type and neutral delays are examined. A mixture of properties of fractional calculus, Laplace transform, and analytical techniques…

Recently, a classical approach to continuous structures has been proposed in [ABBMZ] and [Z] that extends the class of structures falling under the scope of [HI] or [BBHU]. These articles introduce the notion of structures with a standard…

This paper deals with the local existence and uniqueness results for the solution of fractional differential equations with Hilfer-Hadamrd fractional derivative. Using Picard's approximations and generalizing the restrictive conditions…

We consider a general family of nonlocal in space and time diffusion equations with space-time dependent diffusivity and prove convergence of finite difference schemes in the context of viscosity solutions under very mild conditions. The…

In this paper, we prove a new generalized Mikhlin multiplier theorem whose conditions are given with respect to fractional derivatives in integral forms with two different integration intervals. We also discuss the connection between…

Coherence is a fundamental notion in quantum mechanics, defined relative to a reference basis. As such, it does not necessarily reveal the locality of interactions nor takes into account the accessible operations in a composite quantum…

Multifractional processes extend the concept of fractional Brownian motion by replacing the constant Hurst parameter with a time-varying Hurst function. This extension allows for modulation of the roughness of sample paths over time. The…

We describe a new class of self-similar symmetric $\alpha$-stable processes with stationary increments arising as a large time scale limit in a situation where many users are earning random rewards or incurring random costs. The resulting…

In this paper, We study an one--dimensional morphogenesis model considered by C. Stinner et al. in (Math. Meth. Appl. Sci. 2012,35 (445-465). Under homogeneous boundary conditions, we prove the existence of nonconstant positive steady…

We give necessary and sufficient conditions for a multivariate stationary stochastic process to be completely regular. We also give the answer to a question of V.V. Peller concerning the spectral measure characterization of such processes.

In this work, we investigate the fine regularity of L\'evy processes using the 2-microlocal formalism. This framework allows us to refine the multifractal spectrum determined by Jaffard and, in addition, study the oscillating singularities…

A stochastically continuous process $\xi(t)$, $t\geq0$, is said to be time-stable if the sum of $n$ i.i.d. copies of $\xi$ equals in distribution to the time-scaled stochastic process $\xi(nt)$, $t\geq0$. The paper advances the…

This work deals with the finite time stability of generalized proportional fractional systems with time delay. First, based on the generalized proportional Gr\"onwall inequality, we derive an explicit criterion that enables the system…

The concept of local fractional derivative was introduced in order to be able to study the local scaling behavior of functions. However it has turned out to be much more useful. It was found that simple equations involving these operators…

We consider a discrete time dynamic system described by a difference equation with periodic coefficients and with additive stochastic noise. We investigate the possibility of the periodicity for the solution. In particular, we found…

We study the `local entanglement' remaining after filtering operations corresponding to imperfect measurements performed by one or both parties, such that the parties can only determine whether or not the system is located in some region of…

In this paper, we consider a continuous-time Markov process and prove a local limit theorem for the integral of a time-inhomogeneous function of the process. One application is in the study of the fast-oscillating perturbations of linear…

The conserved Swift-Hohenberg equation with cubic nonlinearity provides the simplest microscopic description of the thermodynamic transition from a fluid state to a crystalline state. The resulting phase field crystal model describes a…

We develop a transfer operator-based method for the detection of coherent structures and their associated lifespans. Characterising the lifespan of coherent structures allows us to identify dynamically meaningful time windows, which may be…