Abstract
Using fundamental formulae of iterated fractional Caputo type calculus, we establish several important fractional representation formulae, included iterated ones. Based on these we derive: a whole family of fractional Opial type inequalities, Hilbert-Pachpatte type fractional inequalities, Ostrowski type fractional inequalities, Poincaré and Sobolev type fractional inequalities, finally we give Grüss type fractional inequalities.
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References
Anastassiou, G.A.: Quantitative Approximations. Chapman & Hall/CRC, Boca Raton, New York (2001)
Anastassiou, G.: On right fractional calculus. Chaos, Solitons Fractals 42, 365–376 (2009)
Anastassiou, G.: Fractional Differentiation Inequalities. Springer, New York (2009)
Anastassiou, G.: Fractional representation formulae and right fractional inequalities. Math. Comput. Model. 54(11–12), 3098–3115 (2011)
Anastassiou, G.: Opial type inequalities for functions and their ordinary and balanced fractional derivatives. J. Comput. Anal. Appl. 14(5), 862–879 (2012)
Anastassiou, G.: Advanced fractional Taylor’s formulae. J. Comput. Anal. Appl. (2015)
Anastassiou, G., Argyros, I.: A convergence analysis for a certain family of extended iterative methods: Part II. Applications to fractional calculus. Ann. Univ. Sci. Bp. Sect. Comp. (2015)
Diethelm, K.: The Analysis of Fractional Differential Equations, 1st edn., vol. 2004. Lecture Notes in Mathematics, New York, Heidelberg (2010)
Odibat, Z.M., Shawagleh, N.J.: Generalized Taylor’s formula. Appl. Math. Comput. 186, 286–293 (2007)
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Anastassiou, G.A. (2016). Basic Iterated Fractional Inequalities. In: Anastassiou, G., Duman, O. (eds) Intelligent Mathematics II: Applied Mathematics and Approximation Theory. Advances in Intelligent Systems and Computing, vol 441. Springer, Cham. https://doi.org/10.1007/978-3-319-30322-2_29
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DOI: https://doi.org/10.1007/978-3-319-30322-2_29
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