We extended the classical Bernoulli and Euler numbers and polynomials to introduce the Laguerre-type Bernoulli and Euler numbers and related fractional polynomials. The case of fractional Bernoulli and Euler polynomials and numbers has already been c...
We review some analytic, measure-theoretic and topological techniques for studying ergodicity and entropy of discrete dynamical systems, with a focus on Boole-type transformations and their generalizations. In particular, we present a new proof of th...
In this paper, we further study the generating function involving a variety of special numbers and ploynomials constructed by the second author. Applying the Mellin transformation to this generating function, we define a new class of zeta type functi...
This paper presents a novel algorithm about the industrial robot contouring control based on the NURBS (non-uniform rational B-spline) curve. First, aiming at the error between the industrial robot’s actual trajectory and the desired trajectory...
The paper demonstrates symmetric integral operator and interpolation based numerical approximations for linear and nonlinear ordinary differential equations (ODEs) with oscillatory factor
This paper systematically studies the exact analytical solutions of the (2+1)-dimensional generalized Burgers–Fisher (gBF) equation. Using the Lie symmetry analysis method, the infinitesimal generators of the equation are derived. Through symme...
In this paper, two types of fractional-order damping are proposed for a single flexible link: internal and external friction, related to the material of the link and the environment, respectively. Considering these dampings, the Laplace transform is...
The Zoomeron equation plays a significant role in many fields of physics, especially in soliton theory, such as helping to reveal new distinctive properties in different physical phenomena such as fluid dynamics, laser physics, and nonlinear optics....
The Kuralay-II system (K-IIS) plays a pivotal role in modeling sophisticated nonlinear wave processes, particularly in the field of optics. This study introduces novel soliton solutions for the K-IIS, derived using the Riccati–Bernoulli sub-ODE...
Practical applications of piezoelectric vibration energy harvesting systems are required to produce a stable DC output through the nonlinear process of AC-DC rectification. In most simulation studies of such systems, the diodes have been idealised as...
The dynamical wave solutions of the time–space fractional Date–Jimbo–Kashiwara–Miwa (DJKM) equation have been obtained in this article using an innovative and efficient technique including the Riccati–Bernoulli sub-ODE m...
In this study, the optimal q-Homotopy Analysis Method (optimal q-HAM) has been used to investigate fractional Abel differential equations. This article is designed as a case study, where several forms of Abel equations, containing Bernoulli and Ricca...
Microelectromechanical system (MEMS)-based piezoelectric energy harvesting (PEH) devices can convert the mechanical vibrations of their surrounding environment into electrical energy for low-power sensors. This electrical energy is amplified when the...
In order to optimize the operating path of orchard mowers and improve their efficiency, we propose an MI-DBO (multi-strategy improved dung beetle optimization algorithm) to solve the problem of full-coverage path planning for mowers in standardized q...