A Stochastic Fractional Calculus with Applications to Variational Principles
Fractal and Fractional, 2020 We introduce a stochastic fractional calculus. As an application, we present a stochastic fractional calculus of variations, which generalizes the fractional calculus of variations to stochastic processes.
Houssine Zine, Delfim F. M. Torres
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A Fractional Calculus of Variations for Multiple Integrals with Application to Vibrating String [PDF]
Journal of Mathematical Physics, 2010 We introduce a fractional theory of the calculus of variations for multiple integrals. Our approach uses the recent notions of Riemann-Liouville fractional derivatives and integrals in the sense of Jumarie. Main results provide fractional versions of the
Almeida, Ricardo +2 more
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The Legendre condition of the fractional calculus of variations [PDF]
Optimization, 2014 This is a preprint of a paper whose final and definite form will appear in Optimization (ISSN 0233-1934).
Lazo, M. J., Torres, D. F. M.
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Calculus of variations with fractional derivatives and fractional integrals
Applied Mathematics Letters, 2009 We prove Euler-Lagrange fractional equations and sufficient optimality conditions for problems of the calculus of variations with functionals containing both fractional derivatives and fractional integrals in the sense of Riemann-Liouville.
Almeida, R., Torres, D.F.M.
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A Formulation of Noether's Theorem for Fractional Problems of the Calculus of Variations
Journal of Mathematical Analysis and Applications, 2007 Fractional (or non-integer) differentiation is an important concept both from theoretical and applicational points of view. The study of problems of the calculus of variations with fractional derivatives is a rather recent subject, the main result being ...
Agrawal +18 more
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Generalized fractional calculus with applications to the calculus of variations
Computers & Mathematics with Applications, 2012 Submitted 22-Dec-2011; revised 26-Jan-2012; accepted 27-Jan-2012; for publication in Computers and Mathematics with ...
Odzijewicz, T. +2 more
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Discrete direct methods in the fractional calculus of variations
Computers & Mathematics with Applications, 2013 Finite differences, as a subclass of direct methods in the calculus of variations, consist in discretizing the objective functional using appropriate approximations for derivatives that appear in the problem. This article generalizes the same idea for fractional variational problems.
Pooseh, S., Almeida, R., Torres, D.F.M.
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Analysis of hybrid fractional integro-differential equations with application to cholera dynamics [PDF]
Scientific ReportsThis study establishes the existence of solutions for a class of fractional hybrid integro-differential equations governed by the $$\vartheta$$ -Caputo derivative, subject to slit-strip boundary conditions.
Mohamed S. Algolam +4 more
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Fractional Calculus of Variations for Composed Functionals with Generalized Derivatives
Fractal and FractionalThis paper extends the fractional calculus of variations to include generalized fractional derivatives with dependence on a given kernel, encompassing a wide range of fractional operators.
Ricardo Almeida
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Fractional Calculus of Variations: A Novel Way to Look At It [PDF]
Fractional Calculus and Applied Analysis, 2019 In this work we look at the original fractional calculus of variations problem in a somewhat different way. As a simple consequence, we show that a fractional generalization of a classical problem has a solution without any restrictions on the derivative-order $ $.
Rui A C Ferreira
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