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Poincaré–Type Fractional Inequalities

In: Fractional Differentiation Inequalities

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  • George A. Anastassiou

    (University of Memphis, Department Mathematical Sciences)

Abstract

Here we present Poincaré-type fractional inequalities involving fractional derivatives of Canavati, Riemann—Liouville, and Caputo types. The results are general L p inequalities forward and reverse, univariate and multivariate, on a spherical shell. We give applications to ODEs and PDEs. We present also mean Poincaré-type fractional inequalities. This treatment relies on [57].

Suggested Citation

  • George A. Anastassiou, 2009. "Poincaré–Type Fractional Inequalities," Springer Books, in: Fractional Differentiation Inequalities, chapter 17, pages 445-482, Springer.
    • Handle: RePEc:spr:sprchp:978-0-387-98128-4_17
    DOI: 10.1007/978-0-387-98128-4_17
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