Mathematical Modelling of Dengue Transmission with Intervention Strategies Using Fractional Derivatives.

This paper deals with a deterministic mathematical model of dengue based on a system of fractional-order differential equations (FODEs). In this study, we consider dengue control strategies that are relevant to the current situation in Malaysia. They are the use of adulticides, larvicides, destruction of the breeding sites, and individual protection.

Stochastic SIS Modelling: Coinfection of Two Pathogens in Two-Host Communities.

A pathogen can infect multiple hosts. For example, zoonotic diseases like rabies often colonize both humans and animals. Meanwhile, a single host can sometimes be infected with many pathogens, such as malaria and meningitis.

Dynamics and Complexity of a New 4D Chaotic Laser System.

Derived from Lorenz-Haken equations, this paper presents a new 4D chaotic laser system with three equilibria and only two quadratic nonlinearities. Dynamics analysis, including stability of symmetric equilibria and the existence of coexisting multiple Hopf bifurcations on these equilibria, are investigated, and the complex coexisting behaviors of two and three attractors of stable point and chaotic are numerically revealed. Moreover, a conducted research on the complexity of the laser system reveals that the complexity of the system time series can locate and determine the parameters and initial values that show coexisting attractors.

On properties of geodesic semilocal E-preinvex functions.

The authors define a class of functions on Riemannian manifolds, which are called geodesic semilocal E-preinvex functions, as a generalization of geodesic semilocal E-convex and geodesic semi E-preinvex functions, and some of its properties are established. Furthermore, a nonlinear fractional multiobjective programming is considered, where the functions involved are geodesic E--semidifferentiability, sufficient optimality conditions are obtained. A dual is formulated and duality results are proved by using concepts of geodesic semilocal E-preinvex functions, geodesic pseudo-semilocal E-preinvex functions, and geodesic quasi-semilocal E-preinvex functions.

Some new lacunary statistical convergence with ideals.

In this paper, the idea of lacunary [Formula: see text]-statistical convergent sequence spaces is discussed which is defined by a Musielak-Orlicz function. We study relations between lacunary [Formula: see text]-statistical convergence with lacunary [Formula: see text]-summable sequences. Moreover, we study the [Formula: see text]-lacunary statistical convergence in probabilistic normed space and discuss some topological properties.

Topological properties of some sequences defined over 2-normed spaces.

The paper investigates some classes of real number sequences over 2-normed spaces defined by means of Orlicz functions, a bounded sequence of strictly positive real numbers, a multiplier and a normal paranormed sequence space. Relevant properties of such classes have been investigated. Moreover, relationships among different such classes of sequences have also been studied under various parameters and conditions.

The valuation of currency options by fractional Brownian motion.

This research aims to investigate a model for pricing of currency options in which value governed by the fractional Brownian motion model (FBM). The fractional partial differential equation and some Greeks are also obtained. In addition, some properties of our pricing formula and simulation studies are presented, which demonstrate that the FBM model is easy to use.

Some properties for integro-differential operator defined by a fractional formal.

Recently, the study of the fractional formal (operators, polynomials and classes of special functions) has been increased. This study not only in mathematics but extended to another topics. In this effort, we investigate a generalized integro-differential operator [Formula: see text] defined by a fractional formal (fractional differential operator) and study some its geometric properties by employing it in new subclasses of analytic univalent functions.

Note on fractional Mellin transform and applications.

In this article, we define the fractional Mellin transform by using Riemann-Liouville fractional integral operator and Caputo fractional derivative of order [Formula: see text] and study some of their properties. Further, some properties are extended to fractional way for Mellin transform.

On Cℵ-fibrations in bitopological semigroups.

We extend the path lifting property in homotopy theory for topological spaces to bitopological semigroups and we show and prove its role in the C(ℵ)-fibration property. We give and prove the relationship between the C(ℵ)-fibration property and an approximate fibration property. Furthermore, we study the pullback maps for C(ℵ)-fibrations.

An inversion-free method for finding positive definite solution of a rational matrix equation.

A new iterative scheme has been constructed for finding minimal solution of a rational matrix equation of the form X + A*X (-1) A = I. The new method is inversion-free per computing step. The convergence of the method has been studied and tested via numerical experiments.

Generalized equilibrium problem with mixed relaxed monotonicity.

We extend the concept of relaxed α-monotonicity to mixed relaxed α-β-monotonicity. The concept of mixed relaxed α-β-monotonicity is more general than many existing concepts of monotonicities. Finally, we apply this concept and well known KKM-theory to obtain the solution of generalized equilibrium problem.

On generalized difference Hahn sequence spaces.

We construct some generalized difference Hahn sequence spaces by mean of sequence of modulus functions. The topological properties and some inclusion relations of spaces h p ((F, u, Δ(r)) are investigated. Also we compute the dual of these spaces, and some matrix transformations are characterized.