18 research outputs found

Positive Solutions for Boundary Value Problem of Nonlinear Fractional Differential Equation

We are concerned with the existence and nonexistence of positive solutions for the nonlinear fractional boundary value problem: D0+Î±u(t)+Î»a(t)â€‰f(u(t))=0,â€‰0<t<1,â€‚ u(0)=uâ€²(0)=uâ€²(1)=0, where 2<Î±<3 is a real number and D0+Î± is the standard Riemann-Liouville fractional derivative. Our analysis relies on Krasnoselskiis fixed point theorem of cone preserving operators. An example is also given to illustrate the main results

The Fractional SIRC Model and Influenza A

This paper deals with the fractional-order SIRC model associated with the evolution of influenza A disease in human population. Qualitative dynamics of the model is determined by the basic reproduction number, 0. We give a detailed analysis for the asymptotic stability of disease-free and positive fixed points. Nonstandard finite difference methods have been used to solve and simulate the system of differential equations

Existence of Positive Solutions for m-Point Boundary Value Problem for Nonlinear Fractional Differential Equation

We investigate an m-point boundary value problem for nonlinear fractional differential equations. The associated Green function for the boundary value problem is given at first, and some useful properties of the Green function are obtained. By using the fixed point theorems of cone expansion and compression of norm type and Leggett-Williams fixed point theorem, the existence of multiple positive solutions is obtained

On fractional order dengue epidemic model

This paper deals with the fractional order dengue epidemic model. The stability of disease-free and positive fixed points is studied. Adams-Bashforth-Moulton algorithm has been used to solve and simulate the system of differential equations.This project was funded by the Deanship of Scientific Research (DSR), King Abdulaziz University, under Grant no. 3-130/1433HiCiS

Stochastic Analysis of a Hantavirus Infection Model

In this paper, a stochastic Hantavirus infection model is constructed. The existence, uniqueness, and boundedness of the positive solution of the stochastic Hantavirus infection model are derived. The conditions for the extinction of the Hantavirus infection from the stochastic system are obtained. Furthermore, the criteria for the presence of a unique ergodic stationary distribution for the Hantavirus infection model are established using a suitable Lyapunov function. Finally, the importance of environmental noise in the Hantavirus infection model is illustrated using the Milstein method

An Extension of Wright Function and Its Properties

The paper is devoted to the study of the function WÎ±,Î²Î³,Î´(z), which is an extension of the classical Wright function and Kummer confluent hypergeometric function. The properties of WÎ±,Î²Î³,Î´(z) including its auxiliary functions and the integral representations are proven

-Analogue of Wright Function

We introduce a -analogues of Wright function and its auxiliary functions as Barnes integral representations and series expansion. The relations between -analogues of Wright function and some other functions are investigated

Positive Solutions for Fourth Order Boundary Value Problems

Abstract In this paper, we investigate the problem of existence and nonexistence of positive solutions for the nonlinear boundary value problem

Mathematical Modelling of Lesser Date Moth Using Sex Pheromone Traps and Natural Enemies

In this paper, a mathematical model for lesser date moth is proposed and analyzed. The interaction between the date palm tree, lesser date moth, and natural enemy has been investigated. The impact of sex pheromone traps on lesser date moth is demonstrated. Some sufficient conditions are obtained to ensure the local and global stability of equilibrium points. The occurrence of local bifurcation near the equilibrium points is performed using Sotomayorâ€™s theorem. Theoretical results are illustrated using numerical simulations