Fractional Variational Problems of Euler-Lagrange Equations with Holonomic Constrained Systems

<p class="1Body">In this paper, we examined the fractional Euler-Lagrange equations for Holonomic constrained systems. The Euler-Lagrange equations are derived using the fractional variational problem of Lagrange. In addition, we achieved that the classical results were obtained are agreement when fractional derivatives are replaced with the integer order derivatives. Two physical examples are discussed to demonstrate the formalism.</p>

About Lagrangian Formulation of Classical Fields Within Riemann-Liouville Fractional Derivatives

Recently, an extension of the simplest fractional problem and the fractional variational problem of Lagrange was obtained by Agrawal. The first part of this study presents the fractional Lagrangian formulation of mechanical systems and introduce the Levy path integral. The second part is an extension to Agrawal’s approach to classical fields with fractional derivatives. The classical fields with fractional derivatives are investigated by using the Lagrangian formulation. The case of the fractional Schro¨dinger equation is presented.

The Optimal Column

A new numerical search algorithm is presented which is employed to determine optimum shapes for pin-ended columns having elastic behavior. The search algorithm utilizes a gradient search scheme to seek out the optimum solutions. A Lagrange-like solution is given for the Strongest Column Problem of Lagrange.