### FRACTIONAL DERIVATIVES AND FRACTIONAL INTEGRALS (THE WORK OF SCIENCE)

#### Abstract

We discuss regular approaches to the problems and definition of the fractional derivatives and fractional integrals (simply called differ integrals), namely the Riemann-Liouville Fractional derivative and Caputo fractional derivative and fractional integrals. We prove the basic properties of fractional integrals and Fractional derivatives as well as some theorems of the fractional integrals and derivatives including the rules for their compositions and the conditions for the equivalence of various definitions.

The paper focuses on find the approximate values for functions derivatives, when the function order is a negative, illustrate by a some theorems and examples.

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PDF#### References

Miller, K.S.; Ross, B. An Introduction to the Fractional Calculus and Fractional Differential Equations; John Wiley

and Sons: New York, NY, USA, 1993.

Baleanu D., Muslish S. I., Tas K., "Fractional Hamiltonian Analysis of Higher Order Derivatives Systems", Journal of Mathematical Physics, 147(10), 103503, (2006).

Podlubny Igor. Fractional Differential Equations. United States Academy Press C1999.30 p. ISBN 0-12-558840-2.

Kilbas Anatoly A,Srivastava, Hari M,Trojilo ,Juan J, Theory and Applications of Fractional Differential Equations . John van Mill. Nethelands , Elsevier, 2006,523 p, ISBN 978—0444-51832-3.

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