In this paper, a numerical solution based on nonpolynomial cubic spline functions is used for finding the solution of boundary value problems which arise from the problems of calculus of variations. This approximation reduce the problems to an explicit system of algebraic equations. Some numerical examples are also given to illustrate the accuracy and applicability of the presented method. Keyw...

We will discuss the so-called mixed endpoint conditions for variational problems with non-holonomic constraints given by form actions of order greater than one. We will present some results and discuss the inverse problem of Calculus of Variations.

It is shown that the Lagrange’s equations for a Lagrangian system on a Lie algebroid are obtained as the equations for the critical points of the action functional defined on a Banach manifold of curves. The theory of Lagrangian reduction and the relation with the method of Lagrange multipliers are also studied.

This paper builds upon our recent paper on generalized fractional variational calculus FVC . Here, we briefly review some of the fractional derivatives FDs that we considered in the past to develop FVC. We first introduce new one parameter generalized fractional derivatives GFDs which depend on two functions, and show that many of the one-parameter FDs considered in the past are special cases o...

We establish a formal variational calculus of supervariables, which is a combination of the bosonic theory of Gel’fand-Dikii and the fermionic theory in our earlier work. Certain interesting new algebraic structures are found in connection with Hamiltonian superoperators in terms of our theory. In particular, we find connections between Hamiltonian superoperators and NovikovPoisson algebras tha...

The functional type extension of Ekeland’s variational principle [7] due to Zhong [18] is logical equivalent with it.