Results 41 to 50 of about 1,884 (305)
Necessary optimality conditions for fractional difference problems of the calculus of variations [PDF]
, 2010 We introduce a discrete-time fractional calculus of variations. First and second order necessary optimality conditions are established. Examples illustrating the use of the new Euler-Lagrange and Legendre type conditions are given.
Rui A. C. Ferreira +10 more
core +1 more source
Input-output linearization and fractional robust control of a non-linear system [PDF]
, 2001 This article deals with the association of a linear robust controller and an input-output linearization feedback for the control of a perturbed and non-linear system.
Oustaloup, Alain +7 more
core +1 more source
Construction and Evaluation of a Control Mechanism for Fuzzy Fractional-Order PID
Applied Sciences, 2022 In this research, a control mechanism for fuzzy fractional-order proportional integral derivatives was suggested (FFOPID). The fractional calculus application has been used in different fields of engineering and science and showed to be improved in the ...
Mujahed Al-Dhaifallah
doaj +1 more source
Calculus of Variations with Classical and Fractional Derivatives [PDF]
, 2010 We give a proper fractional extension of the classical calculus of variations. Necessary optimality conditions of Euler-Lagrange type for variational problems containing both classical and fractional derivatives are proved. The fundamental problem of the calculus of variations with mixed integer and fractional order derivatives as well as isoperimetric
Tatiana Odzijewicz, Delfim F. M. Torres
openalex +4 more sources
Axioms, 2023 In this paper, a simple and novel fractional-order memristor circuit is established, which contains only resistance, inductance, capacitance and memristor.
Jindong Liu +4 more
doaj +1 more source
Fractional Calculus of Variations and the Brachistochrone Problem
SSRN Electronic Journal, 2018 The Brachistochrone problem was posed by Johann Bernoulli as a challenge in 1697. It is still an appropriate problem as an example for application in many branches of mathematics. The problem was first solved by Newton in 1697 itself. Later this problem was solved by using Euler-Lagrange equation with the Calculus of Variations.
Bhadra Man Tuladhar
openalex +2 more sources
On Λ-fractional variational calculus
Annals of Mathematics and Physics, 2023 Pointing out that Λ-fractional analysis is the unique fractional calculus theory including mathematically acceptable fractional derivatives, variational calculus for Λ-fractional analysis is established. Since Λ-fractional analysis is a non-local procedure, global extremals are only accepted.
KA Lazopoulos, AK Lazopoulos
openaire +1 more source
Advances in Difference Equations, 2017 In this paper, we study the necessary and sufficient optimality conditions for problems of the fractional calculus of variations with a Lagrange function depending on a Caputo-Fabrizio fractional derivative.
Jianke Zhang, Xiaojue Ma, Lifeng Li
doaj +1 more source
Heliyon, 2021 Wind energy is considered as one of the rapidest rising renewable energy systems. Thus, in this paper the wind energy performance is enhanced through using a new adaptive fractional order PI (AFOPI) blade angle controller.
Ahmed M. Shawqran +4 more
doaj +1 more source
Fractional calculus of variations with a generalized fractional derivative [PDF]
Fractional Differential Calculus, 2016 Summary: In this paper, we introduce a generalization of the Hilfer-Prabhakar derivative and obtain the Euler-Lagrange equations and Hamiltonian formulation with respect to this fractional derivative in the theory of fractional calculus of variations. Also, we get a sufficient condition for optimality.
Askari, Hassan, Ansari, Alireza
openaire +2 more sources