Results 21 to 30 of about 1,386 (256)
Further Research for Lagrangian Mechanics within Generalized Fractional Operators
Fractal and Fractional, 2023 In this article, the problems of the fractional calculus of variations are discussed based on generalized fractional operators, and the corresponding Lagrange equations are established.
Chuanjing Song
doaj +1 more source
Fractional Variational Calculus of Variable Order [PDF]
, 2013 We study the fundamental problem of the calculus of variations with variable order fractional operators. Fractional integrals are considered in the sense of Riemann-Liouville while derivatives are of Caputo type.
Odzijewicz, Tatiana +2 more
openaire +2 more sources
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
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
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
The Variable-Order Fractional Calculus of Variations [PDF]
, 2019 This book intends to deepen the study of the fractional calculus, giving special emphasis to variable-order ...
Almeida, Ricardo +2 more
openaire +2 more sources
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
A Generalized Fractional Calculus of Variations
, 2013 This is a preprint of a paper whose final and definitive form will appear in Control and Cybernetics.
Odzijewicz, T. +2 more
openaire +3 more sources
Weighted Generalized Fractional Integration by Parts and the Euler–Lagrange Equation
Axioms, 2022 Integration by parts plays a crucial role in mathematical analysis, e.g., during the proof of necessary optimality conditions in the calculus of variations and optimal control.
Houssine Zine +3 more
doaj +1 more source