Necessary and sufficient conditions for the fractional calculus of variations with Caputo derivatives

By Ricardo Almeida, Delfim F. M. Torres. 2010

255 citations recorded by the source corpus.

Abstract We prove optimality conditions for different variational functionals containing left and right Caputo fractional derivatives. A sufficient condition of minimization under an appropriate convexity assumption is given. An Euler–Lagrange equation for functionals where the lower and upper bounds of the integral are distinct of the bounds of the Caputo derivative is also proved. Then, the fractional isoperimetric problem is formulated with an integral constraint also containing Caputo derivatives. Normal and abnormal extremals are considered.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/5e1535c59c1fa8dad3f576306d394c84dd3a3d2b

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 Computational Theory and Mathematics

In Modeling and Simulation

Citations in the corpus

Variational Methods for the Fractional Sturm--Liouville Problem (2013, unknown): “3 [3].”
FRACTIONAL h-DIFFERENCE EQUATIONS ARISING FROM THE CALCULUS OF VARIATIONS (2011, background): “It is a mathematical subject that has proved to be very useful in applied fields such as economics, engineering, and physics [3, 21, 22, 29].”
Pontryagin maximum principle for general Caputo fractional optimal control problems with Bolza cost and terminal constraints (2020, unknown): “We refer for example to [2, 6, 7, 9, 12, 21, 41, 43, 57] and references therein.”
Extended Riemann-Liouville fractional derivative operator and its applications (2015, background): “…operator with the extended Beta function given by Srivastava et al. [22] and investigate its various (potentially) useful and (presumably) new properties and formulas, for example, integral representations, Mellin transforms, generating functions, and the extended fractional derivative formulas…”