Fractional calculus of variations in terms of a generalized fractional integral with applications to physics
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Publication:437653
DOI10.1155/2012/871912zbMath1242.49019arXiv1203.1961OpenAlexW3102721748WikidataQ56741651 ScholiaQ56741651MaRDI QIDQ437653
Agnieszka B. Malinowska, Delfim F. M. Torres, Tatiana Odzijewicz
Publication date: 18 July 2012
Published in: Abstract and Applied Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1203.1961
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Cites Work
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- Unnamed Item
- Approximation of fractional integrals by means of derivatives
- Generalized fractional calculus with applications to the calculus of variations
- Controllability of nonlinear fractional dynamical systems
- Calculus of variations on time scales with nabla derivatives
- Fractional variational problems from extended exponentially fractional integral
- A periodic functional approach to the calculus of variations and the problem of time-dependent damped harmonic oscillators
- Modified optimal energy and initial memory of fractional continuous-time linear systems
- Discrete-time fractional variational problems
- Necessary optimality conditions for fractional difference problems of the calculus of variations
- New approach to a generalized fractional integral
- Fractional variational problems depending on indefinite integrals
- Fractional variational calculus with classical and combined Caputo derivatives
- Fractional variational problems with the Riesz-Caputo derivative
- Fractional conservation laws in optimal control theory
- Calculus of variations with fractional derivatives and fractional integrals
- Generalized variational problems and Euler-Lagrange equations
- Generalized natural boundary conditions for fractional variational problems in terms of the Caputo derivative
- Fractals and fractional calculus in continuum mechanics
- Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
- The calculus of variations
- Fractional quantum mechanics and Lévy path integrals
- Micropolar continuum mechanics of fractal media
- Carathéodory equivalence, Noether theorems, and Tonelli full-regularity in the calculus of variations and optimal control
- Fractional kinetics: from pseudochaotic dynamics to Maxwell's demon
- Expansion Formulas in Terms of Integer-Order Derivatives for the Hadamard Fractional Integral and Derivative
- Minimal modified energy control for fractional linear control systems with the Caputo derivative
- Fractional Calculus of Variations for Double Integrals
- Continuous limit of discrete systems with long-range interaction
- Fractional embedding of differential operators and Lagrangian systems
- Fractional dynamics of coupled oscillators with long-range interaction
- Fractional statistical mechanics
- Fractional Optimal Control in the Sense of Caputo and the Fractional Noether's Theorem
- A fractional calculus of variations for multiple integrals with application to vibrating string
- Fractional actionlike variational problems
- FRACTIONAL QUANTUM EULER–CAUCHY EQUATION IN THE SCHRÖDINGER PICTURE, COMPLEXIFIED HARMONIC OSCILLATORS AND EMERGENCE OF COMPLEXIFIED LAGRANGIAN AND HAMILTONIAN DYNAMICS
- The random walk's guide to anomalous diffusion: A fractional dynamics approach
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