Taylor Series Solution for Fractal Bratu-Type Equation Arising in Electrospinning Process

Abstract

Electrospinning is a complex process, and it can be modeled by a Bratu-type equation with fractal derivatives by taking into account the solvent evaporation. Though there are many analytical methods available for such a problem, e.g. the variational iteration method and the homotopy perturbation method, a straightforward method with a simple solution process and high accurate results is much needed. This paper applies the Taylor series technology to fractal calculus, and an analytical approximate solution is obtained. A fractal variational principle is also discussed. As the Taylor series is accessible to all non-mathematicians, this paper sheds a bright light on practical applications of fractal calculus.

Application of he’s fractional derivative and fractional complex transform for time fractional Camassa-Holm equation

“…This mathematical technology is easy and can be applied to other time dependent non-linear fractional differential models in science and engineering. The present method can be easily extended to differential equations with fractal derivatives [36][37][38][39][40][41].…”

A periodic solution of the fractional sine-Gordon equation arising in architectural engineering

“…are unknown to be determined later. Employing the two expansions (12) and (13) into the homotopy equation (11) yields the first two unknowns y 0 ðx; tÞ and y 1 ðx; tÞ in the form…”

A short remark on the nonlinear oscillator with a damping term

“…Taylor series method 26,27 Hereby, we introduce He's frequency formulation by Taylor series. [30][31][32][33] He's frequency formulation and its various modifications have been proved to be extremely simple but remarkably accurate. [34][35][36][37][38] For simplicity, we consider the case when b ¼ 0.…”