Entire solutions of a class of algebraic Briot–Bouquet differential equations utilizing majority concept

Abstract

In this effort, the analytic solution of a class of algebraic Briot–Bouquet differential equations (ABBDE) in the open unit disk is investigated by making use of a major theory. The class is presented by the formula $$\begin{aligned}& \alpha _{1}\varphi ^{\prime 3}(z) + \alpha _{2} \varphi ^{ ' 2} (z) \varphi (z) + \alpha _{3} \varphi ^{\prime } (z) \varphi ^{2} (z) +\aleph ^{k}_{\varphi }(z) = 0, \\& \aleph ^{k}_{\varphi }(z):= a_{k} \varphi ^{k}(z)+a_{k-1} \varphi ^{k-1}(z)+\cdots+ a_{1} \varphi (z)+ a_{0}. \end{aligned}$$ α 1 φ ′ 3 ( z ) + α 2 φ 2 ′ ( z ) φ ( z ) + α 3 φ ′ ( z ) φ 2 ( z ) + ℵ φ k ( z ) = 0 , ℵ φ k ( z ) : = a k φ k ( z ) + a k − 1 φ k − 1 ( z ) + ⋯ + a 1 φ ( z ) + a 0 . The conformal analysis (angle-preserving) of the ABBDEs is considered. Analytic outcomes of the ABBDEs are indicated by employing the major method. Some special cases are investigated.

Analytic Studies of a Class of Langevin Differential Equations Dominated by a Class of Julia Fractal Functions

“…The fractal Langevin equation is studied presenting the dynamics of Brownian elements in the long time boundary [22]. Other studies such as an approximate fractal Langevin differential equation are consumed and an approximate solution is indicated [23][24][25][26][27]. In the present study, we aim to investigate the analytic solution of Langevin differential equation by using a Julia fractal functions and other fractal [28][29][30].…”