We introduce stochastic model of chemotaxis by fractional Derivative generalizing the deterministic Keller Segel model. These models include fluctuations which are important in systems with small particle numbers or close to a critical point. In this work, we study nonlinear Dirichlet boundary conditions, and disturbed multiplicative noise. The required results prove existence uniqueness mild s...

HCSP (Hybrid CSP) extends CSP to describe interacting continuous and discrete dynamics. The concurrency with synchronous communications, timing constructs, interrupts, differential equations, and so on, make the behavior of HCSP difficult to specify and verify. In this paper, we propose a Hoare-style calculus for reasoning about HCSP. The calculus includes Duration Calculus formulas to record p...

Following Hilger’s landmark paper [8], a rapidly expanding body of literature has sought to unify, extend, and generalize ideas from discrete calculus, quantum calculus, and continuous calculus to arbitrary time-scale calculus, where a time scale is simply any nonempty closed set of real numbers. This paper illustrates this new understanding by extending some continuous results from differentia...

The current paper recovers dispersive optical solitons in birefringent fibers that are modeled by the Schrödinger–Hirota equation with differential group delay and white noise. Itô Calculus conducts preliminary analysis. G′/G-expansion approach enhanced Kudryashov’s scheme gave way to a wide spectrum of soliton solutions noise component reflected phase soliton.

Calculus via regularizations and rough paths are two methods to approach stochastic integration calculus close pathwise calculus. The origin of theory is purely deterministic, regularization based on deterministic techniques but there still a probability in the background. goal this paper establish connection between stochastically controlled-type processes, concept reminiscent from theory, so-...

Grishin ([9]) proposed enriching the Lambek calculus with multiplicative disjunction (par) and coresiduals. Applications to linguistics were discussed by Moortgat ([14]), who spoke of the Lambek-Grishin calculus (LG). In this paper, we adapt Girard’s polarity-sensitive double negation embedding for classical logic ([7]) to extract a compositional Montagovian semantics from a display calculus fo...

In this paper, a new variational model for restoring blurred images with multiplicative noise is proposed. Based on the statistical property of the noise, a quadratic penalty function technique is utilized in order to obtain a strictly convex model under a mild condition, which guarantees the uniqueness of the solution and the stabilization of the algorithm. For solving the new convex variation...