A Stochastic Fractional Calculus with Applications to Variational Principles [PDF]
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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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).
Delfim F M Torres, Matheus Lazo
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Generalized transversality conditions in fractional calculus of variations [PDF]
Communications in Nonlinear Science and Numerical Simulation, 2013 This is a preprint of a paper whose final and definite form will be published in Communications in Nonlinear Science and Numerical Simulation, accepted 14-July ...
Ricardo Almeida, Agnieszka B Malinowska
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Generalized fractional calculus with applications to the calculus of variations
Computers and Mathematics With Applications, 2012 Submitted 22-Dec-2011; revised 26-Jan-2012; accepted 27-Jan-2012; for publication in Computers and Mathematics with ...
Delfim F M Torres +2 more
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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 $α$.
R A C Ferreira, Ferreira Rui A C
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The Variable-Order Fractional Calculus of Variations [PDF]
SpringerBriefs in Applied Sciences and Technology, 2019 This book intends to deepen the study of the fractional calculus, giving special emphasis to variable-order ...
Delfim F M Torres +2 more
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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.
Delfim F M Torres, Ricardo Almeida
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Discrete direct methods in the fractional calculus of variations
Computers and 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.
Delfim F M Torres +2 more
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Enhancing variable frequency drive efficiency using fractional hybrid Particle Swarm Optimization and comprehensive thermal management [PDF]
Scientific ReportsThis study proposes a Fractional Calculus Hybrid Approach to enhance the dynamic and thermal performance of vector-controlled Permanent Magnet Synchronous Motor (PMSM) drives.
Kashif Habib +6 more
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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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