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While the definition of a fractional integral may be codified by Riemann andLiouville, an agreed-upon fractional derivative has eluded discovery for manyyears. This is likely a result of integral definitions including numerousconstants of integration in their results. An elimination of constants ofintegration opens the door to an operator that reconciles all known fractionalderivatives and shows surprising results in areas unobserved before, includingthe appearance of the Riemann Zeta Function and fractional Laplace and FourierTransforms. A new class of functions, known as Zero Functions and closelyrelated to the Dirac Delta Function, are necessary for one to performelementary operations of functions without using constants. The operator alsoallows for a generalization of the Volterra integral equation, and provides amethod of solving for Riemann's "complimentary" function introduced during hisresearch on fractional derivatives.

A novel approach to fractional calculus: utilizing fractional integrals and derivatives of the Dirac delta function