Sufficient conditions for variational problems with delayed argument

1993 ◽  
Vol 76 (1) ◽  
pp. 131-144 ◽  
Author(s):  
W. L. Chan ◽  
S. P. Yung
Keyword(s):  
Sufficient Conditions ◽  
Variational Problems ◽  
Delayed Argument

scholarly journals Variational Problems with Partial Fractional Derivative: Optimal Conditions and Noether’s Theorem

2018 ◽  
Vol 2018 ◽  
pp. 1-14
Author(s):  
Jun Jiang ◽  
Yuqiang Feng ◽  
Shougui Li
Keyword(s):  
Fractional Derivative ◽  
Sufficient Conditions ◽  
Variational Problems ◽  
Necessary And Sufficient Conditions ◽  
Optimal Conditions ◽  
Lagrange Equations ◽  
Noether’S Theorem ◽  
Noether's Theorem ◽  
Necessary And Sufficient

In this paper, the necessary and sufficient conditions of optimality for variational problems with Caputo partial fractional derivative are established. Fractional Euler-Lagrange equations are obtained. The Legendre condition and Noether’s theorem are also presented.

scholarly journals Efficiency for Vector Variational Quotient Problems with Curvilinear Integrals on Riemannian Manifolds via Geodesic Quasiinvexity

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1054
Author(s):  
Tiziana Ciano ◽  
Massimiliano Ferrara ◽  
Ştefan Mititelu ◽  
Bruno Antonio Pansera
Keyword(s):  
Riemannian Manifolds ◽  
Sufficient Conditions ◽  
Variational Problems ◽  
Invex Set ◽  
Fractional Variational Problems ◽  
Efficiency Conditions

In the paper, we analyze the necessary efficiency conditions for scalar, vectorial and vector fractional variational problems using curvilinear integrals as objectives and we establish sufficient conditions of efficiency to the above variational problems. The efficiency sufficient conditions use of notions of the geodesic invex set and of (strictly, monotonic) ( ρ , b)-geodesic quasiinvex functions.

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