Taylor series solution for Lane–Emden equation

Release oscillation in a hollow fiber – Part 2: The effect of its frequency on ions release and experimental verification

“…The main effect affecting the frequency is the fiber length; a longer fiber requires a lower frequency and a longer release period. The unsmooth inner surface can be more effectively modeled by fractal calculus, 14 which can reveal some properties beyond the traditional calculus. Fractal calculus and fractional calculus are main tools to deal with discontinuous problems.…”

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.…”

Some General Theorems for Compact Acyclic Multifunctions

“…Now Ω = ∅ (see (8)) is compact, Ω ∩ (X \ U) = ∅, and since X is Tychonoff there exists a (continuous) map σ : X → [0, 1] with σ(Ω) = 1 and σ(X\U) = 0. Let Ψ :…”

“…As a result, our theory can be applied when considering variation methods, iteration methods, perturbation methods, degree theory methods, upper and lower solution methods, etc. (see for example [8][9][10]). Many problems which arise naturally in applications can be formulated in the form x ∈ F x and we can relate it to a simpler problem via the family of problems x ∈ λ F x, 0 ≤ λ ≤ 1.…”