Introduction to the Fractional Calculus of Variations

By Agnieszka B. Malinowska, Delfim F. M. Torres. 2012

374 citations recorded by the source corpus.

Subfields: Atomic and Molecular Physics, and Optics, Modeling and Simulation, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/fdbc32057695b3033faf3f16ff4360effd53a14c

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In Atomic and Molecular Physics, and Optics

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Citations in the corpus

A new Definition of Fractional Derivative without Singular Kernel (2015, background): “[15], Torres and Malinowska [16], Ying and Chen [17]) and by the notable diffusion as shown by the many meetings dedicated to it and the plethora of articles appeared in mathematical (e.”
A discrete method to solve fractional optimal control problems (2014, background): “For more on the subject we refer the reader to [7, 9, 10, 15].”
Existence of a weak solution for fractional Euler-Lagrange equations (2012, background): “Concerning the state of the art on the fractional calculus of variations and respective fractional Euler–Lagrange equations, we refer the reader to the recent book [18].”
Fractional order optimal control problems with free terminal time (2013, background): “For the state of the art on fractional order optimal control, see the recent book [15].”
Variational problems of Herglotz type with time delay: DuBois-Reymond condition and Noether's first theorem (2015, background): “For the importance to include nonconservativism in the calculus of variations, we refer the reader to [26].”
Pontryagin maximum principle for fractional ordinary optimal control problems (2014, background): “This is exactly the same in the fractional context considered in this paper, where the literature concerning the fractional calculus of variations is very rich and already well established (see [6] and references therein).”
Variational Methods for the Fractional Sturm--Liouville Problem (2013, background): “Since then, many papers have been written on the subject, for state of the art in the fractional calculus of variations, we refer the reader to a recent book [14].”
Application of the Local Fractional Series Expansion Method and the Variational Iteration Method to the Helmholtz Equation Involving Local Fractional Derivative Operators (2013, background): “Fractional calculus theory [12–26] has been applied to deal with the differentiable models from the practical engineering discipline, which are the anomalous and fractal physical phenomena.”
Numerical solution of fractional Sturm-Liouville equation in integral form (2014, neutral): “Other applications of fractional variational principles are presented in [2, 19, 25, 26, 28].”
Sobolev Type Fractional Dynamic Equations and Optimal Multi-Integral Controls with Fractional Nonlocal Conditions (2014, methodology): “The reader interested in the development of the theory, methods, and applications of fractional calculus is referred to the books [2, 11, 16, 18, 22, 23, 31, 32, 34] and to the papers [1, 17, 21, 24, 28, 33, 35, 40].”
Fractional Calculus: Quo Vadimus? (Where are we Going?) (2015, result): “We have taken the present occasion, as a compliment to our previous survey [107], to cite books published during the years 2011 [92, 80, 44, 26, 65, 47, 5, 106, 117], 2012 [7, 3, 77, 1, 51, 38, 102, 56, 122, 15, 112, 110, 118], 2013 [14, 18, 89, 29, 36], and 2014 [57, 4, 121, 39, 105, 40, 66, 86, 2,”
Science metrics on fractional calculus development since 1966 (2013, background): “Figure 2 (left) depicts the evolution of Da [19, 12, 56, 75, 57, 99, 60, 87, 100, 100, 77, 68, 85, 95, 69, 70, 71, 72, 78, 23, 102, 13, 96, 64, 114, 36, 79, 73, 91, 63, 84, 80, 105, 109, 4, 111, 82, 22, 27, 28, 110, 81, 67, 32, 29, 86, 52, 33, 117, 106, 55, 58, 112, 113, 108, 6, 15, 2, 41, 59, 10, 4”
Pontryagin maximum principle for general Caputo fractional optimal control problems with Bolza cost and terminal constraints (2020, neutral): “We refer for example to [2, 6, 7, 9, 12, 21, 41, 43, 57] and references therein.”
Fractional optimal control problem for variable-order differential systems (2017, methodology): “We note that the integration by parts technique has been developed and extensively used in the theory of fractional calculus of variations, of which we refer to the monograph in [29].”