Fractional Calculus PP

Fractional Calculus PP

• 1.
  Fractional Optimal ControlProblems: A Simple Application in Fractional Kinetics Vicente Rico-Ramirez Department of Chemical Engineering Instituto Tecnologico de Celaya Mexico
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  1 IntroductionWhat is Fractional Calculus?
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  Fractional Calculus Fractionalcalculus is a generalization of ordinary differentiation and integration to arbitrary NON INTEGER order. Ordinary differentiation: Integer n=1 Non-integer n Fractional differentiation
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  A Bit ofHistory: 1695 (Igor Podlubny) It will lead to a paradox from which one day useful consequences will be drawn What if the order will be n=1/2 ? L’Hopital (1661-1704) Leibniz (1646-1716) ?
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  A Bit ofHistory XVII Century: Leibniz XVIII Century: Euler XIX Century Lagrange, Laplace, Fourier Riemann-Liouville Caputo, 1967 Several mathematicians have contributed with alternative approaches to fractional order differentiation:
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  Fractional Integration Riemann-LiouvilleDefinition Using Laplace Transform F(t) is obtained back through nth-integration of Y(t) Non integer values of n ( renamed as  )
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  Fractional Derivation Riemann-LiouvilleDefinition (Left) Fractional differentiation or order  is expected to be the inverse operation of fractional integration: