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A new Definition of Fractional Derivative and Fractional Integral | ||
| Kirkuk Journal of Science | ||
| Article 1, Volume 13, Issue 1, 2018, Pages 304-323 PDF (0 K) | ||
| DOI: 10.32894/kujss.2018.143047 | ||
| Author | ||
| Ahmed M. Kareem | ||
| Abstract | ||
| 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. | ||
| Keywords | ||
| Gamma function; Beta function; Mittag; Leffler Function; Complementary Error Function; Fractional integration; Riemann; Liouville and Caputo fractional derivatives; Complementary Error; Liouville | ||
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