Fractional Differential Equations

The main purpos e of this chapter is to present a direct and systematic way of finding exact solutions and Backlund transformations of a certain class of nonlinear evolution equations. The nonlinear evolution equations are transformed, by changing the dependent variable(s), into bilinear differential equations of the following special form 
 
$$ F\left( {\frac{\partial }{{\partial t}} - \frac{\partial }{{\partial {t^1}}},\frac{\partial }{{\partial x}} - \frac{\partial }{{\partial {x^1}}}} \right)f(t,x)f({t^1},{x^1}){|_{t = {t^1},x = {x^1}}} = 0 $$ 
 
, which we solve exactly using a kind of perturbational approach.

Direct Methods in Soliton Theory (非線形現象の取扱いとその物理的課題に関する研究会報告)

This review is an elementary introduction to the concepts of the recently developed asymptotic methods and new developments. Particular attention is paid throughout the paper to giving an intuitive grasp for Lagrange multiplier, calculus of variations, optimization, variational iteration method, parameter-expansion method, exp-function method, homotopy perturbation method, and ancient Chinese mathematics as well. Subsequently, nanomechanics in textile engineering and E-innit y theory in high energy physics, Kleiber’s 3/4 law in biology, possible mechanism in spider-spinning process and fractal approach to carbon nanotube are briey introduced. Bubble-electrospinning for mass production of nanob ers is illustrated. There are in total more than 280 references.

An elementary introduction to recently developed asymptotic methods and nanomechanics in textile engineering

A generalized (G′G)-expansion method for the mKdV equation with variable coefficients

Towards hybrid nanofluids: Preparation, thermophysical properties, applications, and challenges

Numerical analysis of magnetic field effects on Eyring-Powell fluid flow towards a stretching sheet

Exact solitary wave solutions for some nonlinear evolution equations via Exp-function method

Effects of magnetic field and wall slip conditions on the peristaltic transport of a Newtonian fluid in an asymmetric channel

Peristaltic transport in an asymmetric channel through a porous medium

A new analytical and numerical treatment for singular two-point boundary value problems via the Adomian decomposition method

Abdelhalim Ebaid

Papers

Numerical analysis of magnetic field effects on Eyring-Powell fluid flow towards a stretching sheet

Exact solitary wave solutions for some nonlinear evolution equations via Exp-function method

Effects of magnetic field and wall slip conditions on the peristaltic transport of a Newtonian fluid in an asymmetric channel

Peristaltic transport in an asymmetric channel through a porous medium

A new analytical and numerical treatment for singular two-point boundary value problems via the Adomian decomposition method