[PDF] Top 20 Computational methods in the fractional calculus of variations and optimal control
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Computational methods in the fractional calculus of variations and optimal control
... Almeida and D. F. M. Torres, A discrete time method to the first variation of fractional order variational functionals, ...Phys, in press ...to the solution of a system ... See full document
193
Calculus of variations of Herglotz type
... thinking and discussion the possibility of writing a thesis and nishing the ...further and produce a more self-contained document if we addressed a nal chapter on Noether's ... See full document
126
Fractional order optimal control problems with free terminal time
... follows. In Section 2 we formulate the optimal con- trol problem under consideration and deduce necessary optimality conditions for it (Theorem ...consists of using the ... See full document
19
Enlarged controllability and optimal control of sub-diffusion processes with Caputo fractional derivatives
... problems in modern science are addressed with the help of optimization ...theory. Optimal control, as a branch of Mathematics, aims to improve the state variables ... See full document
13
Direct transcription methods based on fractional integral approximation formulas for solving nonlinear fractional optimal control problems
... speed of the proposed method depends on the speed one solves the NLP ...On the other hand, a crucial task in solving NLPs is computing the first derivatives of ... See full document
30
A fractional calculus of variations for multiple integrals with application to vibrating string
... nowadays the realm of physicists and mathematicians, who investigate the usefulness of such non-integer order derivatives and integrals in different areas of ... See full document
12
A numerical approach for solving fractional optimal control problems using modified hat functions
... implementation, the method was carried out using Mathematica 11.3. For solving the resulting systems of algebraic equations, the function FindRoot was used in two examples, which are ... See full document
19
Strong minimizers of the calculus of variations on time scales and the Weierstrass condition
... The calculus of variations on time scales was introduced in 2004 with the papers of Bohner [6] and Hilscher and Zeidan ...speaking, in [6] the ... See full document
8
Approximate controllability of impulsive non-local non-linear fractional dynamical systems and optimal control
... controllability and optimal control of a class of impulsive non-local non-linear fractional dynamical systems in Banach ...tional calculus, sectorial operators ... See full document
17
Calculus of variations involving Caputo-Fabrizio fractional differentiation
... order calculus is a generalization of the integer order calculus to a real or complex numbers and, nowadays, it plays an important role in various fields: physics (classic ... See full document
10
A spectral method based on the second kind Chebyshev polynomials for solving a class of fractional optimal control problems
... structure of this paper is arranged in the following way: In Sec- tion 2, an introduction of fractional calculus and properties of the shifted SKCPs ... See full document
13
Application of Bernoulli polynomials for solving variable-order fractional optimal control-affine problems
... variable-order fractional optimal control-affine problems. The variable-order fractional derivative is considered in the Caputo sense, which together with the ... See full document
18
Fractional calculus of variations
... roots of the calculus of variations appear in works of Greek thinkers, such as Queen Dido or Aristotle in the late of the 1st century ...During ... See full document
156
Discrete Direct Methods in the Fractional Calculus of Variations
... to the solution of a system of alge- braic equations. When the system is linear, we can freely increase the number of mesh points, n, and obtain better solutions as long ... See full document
6
Generalized transversality conditions in fractional calculus of variations
... The calculus of variations is concerned with the problem of extremizing ...applications in physics, geometry, engineering, dynamics, control theory, and ... See full document
14
Calculus of variations on time scales and discrete fractional calculus
... direct, in the sense that permits to find directly the optimal solution instead of using variational arguments and go through the usual procedure of solving ... See full document
116
Fractional calculus of variations for double integrals
... The calculus of variations was born in 1697 with the solution to the brachistochrone problem (see, ...area in the XXI century (see, e.g., [7, 13, 21–23]). ... See full document
12
Computational methods for the identification of transcriptional regulation modules
... is of particular interest if we want to have an objective measure to compare sets of sequences in order deter- mine whether one of them is more bound by common motifs than the ...other. ... See full document
187
On the application of optimal control techniques in lossy fieldbuses
... novel control law that is optimal in lossy control networks, in which the actuator applies a generalized linear function of the last applied value whenever there is ... See full document
252
Computational validation of composite methods in the study of molecular properties.
... VALIDATION OF COMPOSITE METHODS IN THE STUDY OF MOLECULAR ...Composite methods using ONIOM and different basis sets have been used to calculate proton and electron ... See full document
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