Title: Necessary and sufficient conditions for calculus of variations under interval uncertainty

Authors: Mohammad Heidari; Mohadeseh Ramezanzadeh

Addresses: Young Researchers and Elite Club, Ayatollah Amoli Branch, Islamic Azad University, Amol, Iran ' School of Mathematics and Computer Science, Damghan University, Damghan, Iran

Abstract: In this paper, a complete investigation of necessary and sufficient conditions is discussed on the variational problems under interval uncertainty. More precisely, it is shown that based on the parametric representation of an interval, the interval variational problems can be interpreted as a set of classical variational problems. Finally, to show the ability and significance of this point of view on the necessary and sufficient conditions, two comprehensive examples are proposed, more specifically the Hanging Cable Problem.

Keywords: interval-valued function; parametric representation; calculus of variations; Euler-Lagrange equation; sufficient condition.

DOI: 10.1504/IJRS.2017.088544

International Journal of Reliability and Safety, 2017 Vol.11 No.1/2, pp.1 - 22

Received: 20 May 2017
Accepted: 01 Sep 2017

Published online: 01 Dec 2017 *

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