The Legendre condition of the fractional calculus of variations [PDF]
Optimization, 2014 Fractional operators play an important role in modelling nonlocal phenomena and problems involving coarse-grained and fractal spaces. The fractional calculus of variations with functionals depending on derivatives and/or integrals of noninteger order is ...
Matheus J Lazo, Delfim F M Torres
exaly +7 more sources
A Stochastic Fractional Calculus with Applications to Variational Principles [PDF]
Fractal and Fractional, 2020 We introduce a stochastic fractional calculus. As an application, we present a stochastic fractional calculus of variations, which generalizes the fractional calculus of variations to stochastic processes.
Houssine Zine, Delfim F. M. Torres
doaj +8 more sources
Calculus of variations with fractional derivatives and fractional integrals [PDF]
Applied Mathematics Letters, 2009 We prove the Euler-Lagrange fractional equations and the sufficient optimality conditions for problems of the calculus of variations with functionals containing both fractional derivatives and fractional integrals in the sense of Riemann-Liouville ...
Ricardo Almeida, Delfim F M Torres
exaly +8 more sources
Isoperimetric problems of the calculus of variations with fractional derivatives [PDF]
Acta Mathematica Scientia, 2012 In this article, we study isoperimetric problems of the calculus of variations with left and right Riemann-Liouville fractional derivatives. Both situations when the lower bound of the variational integrals coincide and do not coincide with the lower ...
Ricardo Almeida +2 more
exaly +6 more sources
Generalized transversality conditions in fractional calculus of variations [PDF]
Communications in Nonlinear Science and Numerical Simulation, 2012 Problems of calculus of variations with variable endpoints cannot be solved without transversality conditions. Here, we establish such type of conditions for fractional variational problems with the Caputo derivative.
Ricardo Almeida, Agnieszka B. Malinowska
core +7 more sources
The Variable-Order Fractional Calculus of Variations [PDF]
, 2018 This book intends to deepen the study of the fractional calculus, giving special emphasis to variable-order ...
Ricardo Almeida +2 more
core +7 more sources
A fractional calculus of variations for multiple integrals with application to vibrating string [PDF]
Journal of Mathematical Physics, 2010 We introduce a fractional theory of the calculus of variations for multiple integrals. Our approach uses the recent notions of Riemann-Liouville fractional derivatives and integrals in the sense of Jumarie. The main results provide fractional versions of
Ricardo Almeida +2 more
exaly +4 more sources
Generalized fractional calculus with applications to the calculus of variations
Computers and Mathematics With Applications, 2012 We study operators that are generalizations of the classical Riemann–Liouville fractional integral, and of the Riemann–Liouville and Caputo fractional derivatives.
Tatiana Odzijewicz +2 more
exaly +6 more sources
A formulation of Noether's theorem for fractional problems of the calculus of variations [PDF]
Journal of Mathematical Analysis and Applications, 2007 Fractional (or non-integer) differentiation is an important concept both from theoretical and applicational points of view. The study of problems of the calculus of variations with fractional derivatives is a rather recent subject, the main result being ...
Gastao S F Frederico, Delfim F M Torres
exaly +3 more sources
A survey on fractional variational calculus [PDF]
, 2019 Main results and techniques of the fractional calculus of variations are surveyed. We consider variational problems containing Caputo derivatives and study them using both indirect and direct methods.
Ricardo Almeida, Delfim F. M. Torres
core +6 more sources