Integration by parts plays a crucial role in mathematical analysis, e.g., during the proof of necessary optimality conditions calculus variations and optimal control. Motivated this fact, we construct new, right-weighted generalized fractional derivative Riemann-Liouville sense with its associated integral for recently introduced weighted Mittag-Leffler kernel. We rewrite these operators equiva...

The need of power and equipment that can serve to distribute the electric energy becomes primordial things this period almost domains’ specialists work in, one is microgrid system gain more places in not just industrial area but domestic area, however, rural or urban. This be worked synchronization with main grid alone provides its own needs alimentation characteristics via distributed generato...

This paper is has addressed the Single Flexible Link Robot. The dynamical model is derived using Euler-Lagrange equation and then a proper controller is designed to suppress a  vibration based-on Input-Shaping (IS) method. But, IS control method is an open loop strategy. Due to the weakness of open loop control systems, a closed loop IS control system is proposed. The achieved closed loop c...

Trajectory optimization is a complex process that includes an infinite number of possibilities and combinations. This work focuses on particular aspect the trajectory optimization, related to velocity along predefined path, with aim minimizing power consumption. To tackle problem, functional formulation minimization strategy developed, by means Euler-Lagrange equation. The later performed using...

This article proposes and analyses distributed, leaderless, model-independent consensus algorithms for networked Euler–Lagrange systems. We propose a fundamental consensus algorithm, a consensus algorithm accounting for actuator saturation, and a consensus algorithm accounting for unavailability of measurements of generalised coordinate derivatives, for systems modelled by Euler–Lagrange equati...

This article presents the problem of quickest descent, or the Brachistochrone curve, that may be solved by the calculus of variations and the Euler-Lagrange equation. The cycloid is the quickest curve and also has the property of isochronism by which Huygens improved on Galileo’s pendulum. AMS Subject Classification: 34A02, 00A09, 97A20

Leonhard Euler called (1) Pell’s Equation after the English mathematician John Pell (1611-1685). This terminology has persisted to the present day, despite the fact that it is well known to be mistaken: Pell’s only contribution to the subject was the publication of some partial results of Wallis and Brouncker. In fact the correct names are the usual ones: the problem of solving the equation was...

Unusual stabilized nite element methods are introduced here for linear second order equations. The method consists in subtracting to the standard Galerkin method a mesh dependent term composed by the adjoint operator applied to the test function multiplied by the residual of the Euler-Lagrange equation. The method is numerically tested for advective dominated and zero order dominated regimes, w...

An analytical expression for the optimal control of an Ebola problem is obtained. The analytical solution is found as a first-order approximation to the Pontryagin Maximum Principle via the Euler–Lagrange equation. An implementation of the method is given using the computer algebra system Maple. Our analytical solutions confirm the results recently reported in the literature using numerical met...