Abstract In this work, a nonlinear singular variable-order fractional Emden–Fowler equation involved with derivative non-singular kernel (in the Atangana–Baleanu–Caputo type) is introduced and computational method proposed for its numerical solution. The desired established upon shifted Jacobi polynomials their operational matrix of differentiation (which extracted in present study) together sp...

The current due to cold tunneling of electrons from a metallic surface exposed high electric fields, regularly named ``dark current,'' is commonly described in modern literature using an analytical approximate solution provided by Murphy and Good [Phys. Rev. 102, 1464 (1956)]. This expression, which corrects earlier work Fowler Nordheim, Fowler-Nordheim-type equation: $I\ensuremath{\sim}{E}^{2}...

BACKGROUND Anatomical dead space is usually measured using the Fowler equal area method. Alternative methods include the Hatch, Cumming, and Bowes methods, in which first, second, and third order polynomials, respectively, fitted to an expired CO2 volume vs expired volume curve, intercept the x-axis at the anatomical dead space. This study assessed systematic errors and susceptibility to noise ...

αu(0)−β u(0) = 0, γu(1)+ δu(1) = 0, (2) where α,β ,γ,δ ≥ 0,λ ∈ R and ρ := γβ + αγ + αδ > 0; p ∈ C((0,1), [0,∞)) and may be singular at t = 0,t = 1. When λ < 0, see [3,4,7,8] for the result concerning the above problem. When λ > 0, [6] shows the existence and uniqueness to (1) and (2) in the case of β = δ = 0 by means of the shooting method. For the following problem u + p(t)u−λ(t)+ q(t)u(t) = 0...

Article history: Received 28 May 2010 Available online 16 September 2010 Submitted by Goong Chen

We consider the following anisotropic Emden-Fowler equation ∇(a(x)∇u) + εa(x)e = 0 in Ω, u = 0 on ∂Ω, where Ω ⊂ R is a smooth bounded domain and a is a positive smooth function. We study here the phenomenon of boundary bubbling solutions which do not exist for the isotropic case a ≡ constant. We determine the localization and asymptotic behavior of the boundary bubbles, and construct some bound...

Numerical continuation calculations for ordinary differential equations (ODEs) are, by now, an established tool for bifurcation analysis in dynamical systems theory as well as across almost all natural and engineering sciences. Although several excellent standard software packages are available for ODEs, there are for good reasons no standard numerical continuation toolboxes available for parti...

Numerical continuation calculations for ordinary differential equations (ODEs) are, by now, an established tool for bifurcation analysis in dynamical systems theory as well as across almost all natural and engineering sciences. Although several excellent standard software packages are available for ODEs, there are for good reasons no standard numerical continuation toolboxes available for parti...