[PDF] Top 20 Calculus of variations on time scales and discrete fractional calculus
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Calculus of variations on time scales and discrete fractional calculus
... 1937 and Stefan Hilger accomplished it in his PhD thesis [60] in ...a time scale as a nonempty closed subset of the real numbers and on such sets he defined a (delta) ∆-derivative ... See full document
116
Computational methods in the fractional calculus of variations and optimal control
... lems. On one hand, there are the direct methods. In a branch of direct methods, the problem is discretized on the interested time interval using discrete values of the unknown ... See full document
193
A fractional calculus of variations for multiple integrals with application to vibrating string
... depend on functions of two or more variables arise in a natural way, ...degrees of freedom 共string, membranes, ...0 and x = L. Let us denote the transverse displacement of the particle ... See full document
12
Existence and uniqueness results for a fractional Riemann-Liouville nonlocal thermistor problem on arbitrary time scales
... theories of difference and differential equations into a single the- ...A time scale is a model of time, and the theory has found important applications in several contexts that ... See full document
5
Symmetric quantum calculus
... classical calculus, there are some attempts to define a symmetric integral: see, for example, ...In discrete time we have some examples of symmetric integrals, namely the q-symmetric integral: ... See full document
138
A time-fractional Borel-Pompeiu formula and a related hypercomplex operator calculus
... equations of mathematical-physics. In particular, we have the work of G¨ urlebeck and Spr¨ oßig based on a Borel-Pompeiu formula and on an orthogonal decomposition of the ... See full document
22
A fractional calculus of variations for multiple integrals with application to vibrating string
... work of Riewe [38]. Riewe formulated the problem of the calculus of variations with fractional derivatives and obtained the respective Euler-Lagrange equations, combining ... See full document
12
Isoperimetric problems of the calculus of variations with fractional derivatives
... Riemann-Liouville fractional derivative is infinite at x = a if y(a) 6= ...Riemann-Liouville fractional derivative is also not finite at x = b ...left fractional derivatives, then necessarily y(a) = ... See full document
13
Generalized transversality conditions in fractional calculus of variations
... stated and proved in the remaining ...Bolza-type fractional variational problem and develop the transversality conditions in a compact ...type of variable terminal ...for fractional ... See full document
14
Calculus of variations of Herglotz type
... with time delay are very important in modelling real-life phenomena in several elds, such as mathematics, biology, chemistry, economics and ...present time, but also by its behaviour in the ... See full document
126
Linear fractional discrete-time systems
... meaning) of derivatives and integrals of fractional order since the beginnings of differential ...concepts of fractional calculus have been developed and ... See full document
6
A formulation of Noether's theorem for fuzzy problems of the calculus of variations
... fuzzy calculus of variations extends the classical variational calculus by con- sidering fuzzy variables and their derivatives into the variational integrals to be ...problems of ... See full document
13
Existence and uniqueness of solution for a fractional Riemann-Liouville initial value problem on time scales
... theory of general metric spaces, we have for T the fundamental concepts such as open balls (intervals), neighborhoods of points, open sets, closed sets, compact sets, ...ðtÞ of a given point t 2 T is ... See full document
6
A stochastic fractional calculus with applications to variational principles
... theory of the calculus of variations evolved in order to include fractional operators and better describe non-conservative systems in mechanics [ 5 ...] and to [ 7 – 9 ] ... See full document
10
General quantum variational calculus
... smallest discrete quantity of some physical property and it comes from the Latin word ”quantus”, which literally means how ...quantum calculus is usually referred in mathematics as the ... See full document
20
Calculus of variations involving Caputo-Fabrizio fractional differentiation
... Although fractional calculus have various fields of applications, in this paper we are interested in the fractional calculus of variations which deals with optimization ... See full document
10
Calculus of variations on time scales and applications to economics
... absence of a general chain rule on an ar- bitrary time scale causes this impossibility [20, ...problems of the calculus of variations with nabla derivatives and ... See full document
138
Discrete Direct Methods in the Fractional Calculus of Variations
... subclass of direct methods in the calculus of variations, consist in discretizing the objective functional using appropriate approximations for derivatives that appear in the ...for ... See full document
6
Fractional calculus of variations
... the fractional calculus of variations with a Lagrangian depending on fractional derivatives has emerged as an elegant alternative to study non-conservative ...presented ... See full document
156
Fractional calculus of variations for double integrals
... The Fractional Calculus of Variations (FCV) was born in 1996-97 with the proof, by Riewe, of the Euler-Lagrange fractional differential equations [29, ...subject of strong ... See full document
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