In the present paper, we introduce a pair of second order fractional symmetric variational programs over cone constraints and derive weak, strong, and converse duality theorems under second order F-convexity assumptions. Moreover, self duality theorem is also discussed. Our results give natural unification and extension of some previously known results in the literature. | Yugoslav Journal of Operations Research 28 (2018), Number 1, 39-57 DOI: SECOND ORDER SYMMETRIC DUALITY IN FRACTIONAL VARIATIONAL PROBLEMS OVER CONE CONSTRAINTS Anurag JAYSWAL Department of Applied Mathematics, Indian Institute of Technology (Indian School of Mines), Dhanbad-826 004, Jharkhand, India anurag jais123@ Shalini JHA∗ Department of Applied Mathematics, Indian Institute of Technology (Indian School of Mines), Dhanbad-826 004, Jharkhand, India Received: December 2016 / Accepted: June 2017 Abstract: In the present paper, we introduce a pair of second order fractional symmetric variational programs over cone constraints and derive weak, strong, and converse duality theorems under second order F-convexity assumptions. Moreover, self duality theorem is also discussed. Our results give natural unification and extension of some previously known results in the literature. Keywords: Variational problem, Second order F-convexity, Second order duality. MSC: 90C26, 90C29, 90C30, 90C46. 1. INTRODUCTION Duality results in calculus of variations arise in various fields of engineering science such as mechanics, physics, filtering and optimal control theory. It allows us to associate a dual problem with variational problem and to study the relationship between the two problems. In mechanics, duality allows us to describe precisely the relationship between different energy principles which govern certain nonlinear problems. The primal and the dual problems are two well known forms of the conservation principles characterizing the displacements and the constraints, respectively. 40 A. Jayswal, S. Jha / Second Order Symmetric Duality The notion of symmetric duality received several impulse after poineering work of Dorn [7]. Mond and Hanson [15] applied the concept of symmetric duality to variational problems. Kim and Lee [14] formulated a pair of multiobjective nonlinear generalized symmetric .
