In this paper, we introduce three different definitions of fractional derivatives, namely Riemann-Liouville derivative, Caputo derivative and the new formula Caputo expansion formula, and some basics properties of these derivatives are discussed. The difference between Caputo and Riemann – Liouville formulas for the fractional derivatives also mentioned. The paper focuses on find approximate values for function derivatives, when the function order is a negative integer, illustrated by some theorems and examples.
M. Kareem, A. (2018). A new Definition of Fractional Derivative and Fractional Integral. Kirkuk Journal of Science, 13(1), 304-323. doi: 10.32894/kujss.2018.143047
MLA
Ahmed M. Kareem. "A new Definition of Fractional Derivative and Fractional Integral". Kirkuk Journal of Science, 13, 1, 2018, 304-323. doi: 10.32894/kujss.2018.143047
HARVARD
M. Kareem, A. (2018). 'A new Definition of Fractional Derivative and Fractional Integral', Kirkuk Journal of Science, 13(1), pp. 304-323. doi: 10.32894/kujss.2018.143047
VANCOUVER
M. Kareem, A. A new Definition of Fractional Derivative and Fractional Integral. Kirkuk Journal of Science, 2018; 13(1): 304-323. doi: 10.32894/kujss.2018.143047
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