FRACTIONAL DERIVATIVES AND FRACTIONAL INTEGRALS (THE WORK OF SCIENCE)

Afsar Khan

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.


Keywords


Mittag-Leffler functions, Gamma functions, Beta functions and their properties are briefly discussed

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References


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