Truncated V-fractional Taylor's Formula with Applications
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J. Stoer and R. Bulirsch, Introduction to numerical analysis, vol.12. Springer Science & Business Media, New York, 2013.
A. Ralston and P. Rabinowitz, A first course in numerical analysis. Courier Corporation, New York, 2001.
R. Courant and F. John, Introduction to calculus and analysis I. Springer Science & Business Media, New York, 2012.
I. Podlubny, Fractional Differential Equations, Mathematics in Science and Engineering, Academic Press, San Diego, vol. 198. 1999.
E. Capelas de Oliveira and J. A. Tenreiro Machado, A review of definitions for fractional derivatives and integral, Math. Probl. Eng., vol. 2014,, p. (238459), 2014.
R. Herrmann, Fractional calculus: An Introduction for Physicists, World Scientific Publishing Company, Singapore. 2011.
J. A. Tenreiro Machado, And I say to myself: What a fractional world!, Frac. Calc. Appl. Anal., vol. 14,, pp. 635--654, 2011.
M. D. Ortigueira and J. A. Tenreiro Machado, What is a fractional derivative?,'' J. Comput. Phys., vol. 293., pp. 4--13, 2015.
J. Vanterler da C. Sousa and E. Capelas de Oliveira, Mittag-Leffler functions and the truncated V-fractional derivative,'' submitted, (2017).}
U. N. Katugampola, A new fractional derivative with classical properties, arXiv preprint arXiv:1410.6535, 2014.
R. Khalil, M. Al Horani, A. Yousef, and M. Sababheh, A new definition of fractional derivative, J. Comput. and Appl. Math. , vol. 264, pp.65--70, 2014.
J. Vanterler da C. Sousa and E. Capelas de Oliveira, A new truncated M-fractional derivative unifying some fractional derivatives with classical properties,'' submitted, (2017).
J. Vanterler da C. Sousa and E. Capelas de Oliveira, M-fractional derivative with classical properties,'' submitted, (2017).
D. R. Anderson, Taylor's formula and integral inequalities for conformable fractional derivatives, in Contributions in Mathematics and Engineering, in Honor of Constantin Caratheodory, Springer, Berlin 25-43, 2016.
D. R. Anderson, Taylor's formula and integral inequalities for conformable fractional derivatives, arxiv.org/pdf/1409.5888v1, (2014).
W. G. Kelley and A. C. Peterson, The theory of differential equations: classical and qualitative}. Springer Science & Business Media, New York, 2010.
J. M. Steele, The Cauchy-Schwartz master class: an introduction to the art
of mathematical inequalities. Cambridge University Press, New York, 2004.
M. Z. Sarikaya and H. Budak, ``New inequalities of opial type for conformable fractional integrals,'' RGMIA Rearch Report Collection, vol. 19, p.10 pages, 2016.
J. Vanterler da C. Sousa and E. Capelas de Oliveira, ``A truncated V-fractional derivative in R^n,'' submitted, (2017).
DOI: https://doi.org/10.5540/tema.2018.019.03.525
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Trends in Computational and Applied Mathematics
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