Fractional variational calculus and the transversality conditions

By Om Prakash Agrawal. 2006

247 citations recorded by the source corpus.

Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/68c43a94cd21962f8c0f0dc1e88fc0bfd6863360

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Modeling and Simulation

In Numerical Analysis

Citations in the corpus

Necessary and sufficient conditions for the fractional calculus of variations with Caputo derivatives (2010, background): “We also mention [3], where an Euler–Lagrange equation and a transversality condition are given, for functionals with left Caputo derivatives and a boundary condition on the initial point x = a.”
On exact solutions of a class of fractional Euler–Lagrange equations (2007, background): “During the last years the fractional variational principles [12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25] have developed and applied to fractional optimal control problems [26, 27].”
The Variable-Order Fractional Calculus of Variations (2018, background): “Agrawal continued the study of the fractional Euler–Lagrange equations (Agrawal, 2002, 2006, 2007), for some kinds of fractional variational problems, for example, problems with only one dependent variable, for functionals with different orders of fractional derivatives, for several functions,…”
NECESSARY OPTIMALITY CONDITIONS FOR FRACTIONAL DIFFERENCE PROBLEMS OF THE CALCULUS OF VARIATIONS (2010, background): “5 is the discrete analog of the fractional Euler-Lagrange equation of Agrawal [1, Theorem 1]; the natural boundary conditions (22) and (23) are the discrete fractional analogues of the transversality conditions in [3, 21].”
An iterative approach for solving fractional optimal control problems (2018, unknown): “A general formulation for FOCPs was extended by Agrawal (2004, 2006); Agrawal et al. (2010) and Almedia and Torres (2011), where the necessary conditions of optimization are achieved for FOCPs with the Caputo and Riemann–Liouville derivatives.”
A fractional calculus of variations for multiple integrals with application to vibrating string (2010, methodology): “We introduce the fractional nabla operator by ∇αWX = iaD α x [1] + jcD α y [2] + keD α z [3] , where the i, j, k define a fixed right-handed orthonormal basis.”
ADJOINT FRACTIONAL DIFFERENTIAL EXPRESSIONS AND OPERATORS (2007, methodology): “Inspite of the remark made by [1], the definition of the rightsided Caputo derivative did not appear in the literature until very recent works by Agrawal [3, 4] The right-sided Caputo derivative is defined by analogy with the right-sided Riemann–Liouville derivative: C t D α b f (t) = (−1)n Γ(n−α) b”
Optimality conditions and a solution scheme for fractional optimal control problems (2009, background): “In a recent series of papers, Agrawal (2002, 2004, 2006) formulated necessary conditions for optimality, that is Euler-Lagrangian equations, for optimization problems involving fractional derivatives.”
Fractional Optimal Control in the Sense of Caputo and the Fractional Noether's Theorem (2007, methodology): “Using the results obtained in [1, 2, 3], equation (9) is equivalent to”
Variational problems with fractional derivatives: Euler–Lagrange equations (2008, background): “on F have to be supposed. For instance, the condition 4 f(1) = 0 provides the desired equivalence of (6) with (7, 8). (ii) The Lagrangian L(t,u,aDα t u) = (aD α t u−u)2 was investigated in details in [2]. Solutions of the corresponding fractional variational problem (9) can be found directly. It is ”
A numerical scheme for the solution of a class of fractional variational and optimal control problems using the modified Jacobi polynomials (2016, unknown): “Moreover, FVPs in terms of the Riemann–Liouville and Caputo fractional derivatives and for the Riesz fractional derivatives are formulated in Agrawal (2006, 2007a) and Agrawal (2007b), respectively.”