Moustafa El-Shahed

Peristaltic transport of Johnson-Segalman fluid under effect of a magnetic field

The peristaltic transport of Johnson-Segalman fluid by means of an infinite train of sinusoidal waves traveling along the walls of a two-dimensional flexible channel is investigated. The fluid is electrically conducted by a transverse magnetic field. A perturbation solution is obtained for the case in which amplitude ratio is small. Numerical results are reported for various values of the physical parameters of interest.

Nontrivial solutions for a nonlinear multi-point boundary value problem of fractional order

We investigate the existence of nontrivial solutions for a multi-point boundary value problem for fractional differential equations. Under certain growth conditions on the nonlinearity, several sufficient conditions for the existence of nontrivial solution are obtained by using Leray-Schauder nonlinear alternative. As an application, some examples to illustrate our results are given.

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.

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, R0. 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.

Two-dimensional q-differential transformation and its application

The one-dimensional q-differential transformation was introduced in [8] for solving the ordinary q-differential equations. Here, we present the definition and operation of the two-dimensional q-differential transform. A distinctive feature of the q-differential transform is its ability to solve linear and nonlinear partial q-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.

Positive Solutions for Boundary Value Problems of Nonlinear Fractional Differential Equations

In this paper, we investigate the problem of existence and nonexistence of positive solutions for the nonlinear boundary value problem of fractional order: Dαu(t)+λa(t)f(u(t)) = 0, 0<t<1, n−1<α⩽n, n⩾3, u(0) = u″(0) = u‴(0) = … = u(n−1)(0) = 0, γu′(1)+βu″(1) = 0, where Dα is the Caputo’s fractional derivative and λ is a positive parameter. By using Krasnoeselskii’s fixed‐point theorem of cone preserving operators, we establish various results on the existence of positive solutions of the boundary value problem. Under various assumptions on a(t) and f(u(t)), we give the intervals of the parameter λ which yield the existence of the positive solutions. An example is also given to illustrate the main results.