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Fractional Representation Formulae Using Initial Conditions and Fractional Ostrowski Inequalities

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Part of the book series: Studies in Computational Intelligence ((SCI,volume 609))

Abstract

Here we present very general fractional representation formulae for a function in terms of the fractional Riemann-Liouville integrals of different orders of the function and its ordinary derivatives under initial conditions.

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References

  1. G. Anastassiou, M. Hooshmandasl, A. Ghasemi, F. Moftakharzadeh, Montgomery identities for fractional integrals and related fractional inequalities. J. Inequal. Pure Appl. Math. 10(4), Article 97, 6 (2009)

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  2. G.A. Anastassiou, in Fractional Representation Formulae Under Initial Conditions and Fractional Ostrowski Type Inequalities, Demonstratio Mathematica, 2014

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  3. D.S. Mitrinovic, J.E. Pecaric, A.M. Fink, Inequalities for Functions and Their Integrals and Derivatives (Kluwer Academic Publishers, Dordrecht, 1994)

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  4. S. Miller, B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations (Wiley, USA, 1993)

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Correspondence to George A. Anastassiou .

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Anastassiou, G.A. (2016). Fractional Representation Formulae Using Initial Conditions and Fractional Ostrowski Inequalities. In: Intelligent Comparisons: Analytic Inequalities. Studies in Computational Intelligence, vol 609. Springer, Cham. https://doi.org/10.1007/978-3-319-21121-3_5

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  • DOI: https://doi.org/10.1007/978-3-319-21121-3_5

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-21120-6

  • Online ISBN: 978-3-319-21121-3

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