Fractional Calculus
المؤلف:
Butzer, P. L. and Westphal, U.
المصدر:
"An Introduction to Fractional Calculus." Ch. 1 in Applications of Fractional Calculus in Physics (Ed. R. Hilfer). Singapore: World Scientific
الجزء والصفحة:
...
12-8-2018
1980
Fractional Calculus
The study of an extension of derivatives and integrals to noninteger orders. Fractional calculus is based on the definition of the fractional integral as
where 
is the gamma function. From this equation, fractional derivatives can also be defined.
REFERENCES:
Butzer, P. L. and Westphal, U. "An Introduction to Fractional Calculus." Ch. 1 in Applications of Fractional Calculus in Physics (Ed. R. Hilfer). Singapore: World Scientific, pp. 1-85, 2000.
Kilbas, A. A.; Srivastava, H. M.; and Trujiilo, J. J. Theory and Applications of Fractional Differential Equations. Amsterdam, Netherlands: Elsevier, 2006.
McBride, A. C. Fractional Calculus. New York: Halsted Press, 1986.
Nishimoto, K. Fractional Calculus. New Haven, CT: University of New Haven Press, 1989.
Samko, S. G.; Kilbas, A. A.; and Marichev, O. I. Fractional Integrals and Derivatives. Yverdon, Switzerland: Gordon and Breach, 1993.
Oldham, K. B. and Spanier, J. The Fractional Calculus: Integrations and Differentiations of Arbitrary Order. New York: Academic Press,
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