Some Algebra of Leibniz Rule for Fractional Calculus
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- Cauchy Formula, Riemann Liouville Derivative, Caputo Derivative, Generalized Leibniz Rule, Quantization, Projection Operator
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- It is well known that the Leibniz rule has a binomial representation of derivative for the product of two functions. This has an identical form which is the power of sum of two functions. Since the power of sum can be fraction, we can extend the derivative to the fractional power, i.e., Riemann-Liouville derivative and Caputo derivative. And then, the generalized Leibniz rule is derived in which the form is the fractional power of the binomial representation. Moreover, we describe the Riemann-Liouville fractional derivative and Caputo derivative of production of two functions as the sum of integer powers. On the other hand, we introduce the projection operator and calculate some algebra.
Full text: IJISM_591_FINAL.pdf