[PDF] Top 20 Discrete Direct Methods in the Fractional Calculus of Variations
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Discrete Direct Methods in the Fractional Calculus of Variations
... tions. Direct methods, however, to the best of our knowl- edge, have got less interest and are not well ...introduction of using finite differences has been made in Riewe (1996) ... See full document
6
Linear fractional discrete-time systems
... about the existence (and the meaning) of derivatives and integrals of fractional order since the beginnings of differential ...concepts of fractional ... See full document
6
Variational methods for the solution of fractional discrete/continuous Sturm-Liouville problems
... between the fractional Sturm–Liouville difference problem and a constrained discrete fractional variational ...solutions of Sturm–Liouville fractional difference equations by ... See full document
20
A fractional calculus of variations for multiple integrals with application to vibrating string
... started in 1996 with the work of Riewe [38]. Riewe formulated the problem of the calculus of variations with fractional derivatives and obtained ... See full document
12
Direct transcription methods based on fractional integral approximation formulas for solving nonlinear fractional optimal control problems
... problems, the numerical methods for FOCPs can be categorized into “direct” and “indirect” ...indirect methods, the solution is obtained by solving a fractional Hamiltonian ... See full document
30
A fractional calculus of variations for multiple integrals with application to vibrating string
... a fractional theory of the calculus of variations for multiple ...uses the recent notions of Riemann–Liouville fractional derivatives and integrals in ... See full document
12
A stochastic fractional calculus with applications to variational principles
... to the calculus of variations, addressing different optimization problems by means of classical, stochastic, and fractional derivatives through appropriate Euler-Lagrange ... See full document
10
A time-fractional Borel-Pompeiu formula and a related hypercomplex operator calculus
... and the associated time-fractional parabolic Dirac ...introduce the time-fractional analogues of the Teodorescu and Cauchy-Bitsadze operators in a cylindrical domain, and ... See full document
22
Calculus of variations on time scales and applications to economics
... theory of time scales is a relatively new area, that bridges, generalize and extends the traditional discrete dynamical systems ...and the various dialects of q-calculus [41, 74] ... See full document
138
First integrals for problems of calculus of variations on locally convex spaces
... problems of CV have very wide applications in several fields of mathematics, and in many areas of physics, economics, and ...biology. In recent years, part of the ... See full document
12
A higher dimensional fractional Borel‐Pompeiu formula and a related hypercomplex fractional operator calculus
... a fractional integro-differential operator calculus for Clifford-algebra valued ...introduce fractional analogues of the Teodorescu and Cauchy-Bitsadze operators and we investigate some ... See full document
21
Strong minimizers of the calculus of variations on time scales and the Weierstrass condition
... interested in the theory of time scales is referred to [10,11], while for the classical continuous-time calculus of variations we refer to [12,19], and for the ... See full document
8
A conformable fractional calculus on arbitrary time scales
... A fractional calculus, that is, a study of differentiation and integration of non-integer order, is here investigated via the recent and powerful calculus on time ...new ... See full document
6
Computational methods in the fractional calculus of variations and optimal control
... on fractional optimal control problems by considering the end time, T , free and the dynamic control system ...and fractional order derivatives. For convenience, we consider the ... See full document
193
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
Calculus of variations on time scales and discrete fractional calculus
... to the discrete fractional calculus theory we proved some properties for the fractional sum and difference operators in Section ...then, in Section 7.3, we proved ... See full document
116
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 ...economics. ... See full document
14
Fractional calculus of variations
... In the recent years, the fractional calculus of variations with a Lagrangian depending on fractional derivatives has emerged as an elegant alternative to study ... See full document
156
Fractional calculus of variations in terms of a generalized fractional integral with applications to physics
... In Sections 4, 5, and 6 we study three important classes of generalized variational problems: we obtain fractional Euler-Lagrange conditions for the fundamental Section 4 and generalized[r] ... See full document
24
Isoperimetric problems of the calculus of variations with fractional derivatives
... 1. The left Riemann-Liouville fractional derivative is infinite at x = a if y(a) 6= ...then the right Riemann-Liouville fractional derivative is also not finite at x = b ...that the ... See full document
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