Abstract
Here we introduce and study the right and left fuzzy fractional Riemann- Liouville integrals and the right and left fuzzy fractional Caputo derivatives. Then we present the right and left fuzzy fractional Taylor formulae. Based on these we establish a fuzzy fractional Ostrowski type inequality with applications. The last inequality provides an estimate for the deviation of a fuzzy real number valued function from its fuzzy average, and the related upper bounds are given in terms of the right and left fuzzy fractional derivatives of the involved function. The purpose of embedding fuzziness into fractional calculus and have them act together, is to better understand, explain and describe the imprecise, uncertain and chaotic phenomena of the real world and then derive useful conclusions. This chapter is based on [54].
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© 2011 Springer-Verlag Berlin Heidelberg
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Anastassiou, G.A. (2011). Fuzzy Fractional Calculus and the Ostrowski Integral Inequality. In: Intelligent Mathematics: Computational Analysis. Intelligent Systems Reference Library, vol 5. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17098-0_34
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DOI: https://doi.org/10.1007/978-3-642-17098-0_34
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-17097-3
Online ISBN: 978-3-642-17098-0
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