Affiliation:
1. Community College of Qatar, Qatar
Abstract
In this chapter, the author introduces a concept of apparent measure in R^n and associates the concept of relative dimension (of real order) that depends on the geometry of the object to measure and on the distance that separates it from an observer. At the end, the author discusses the relative dimension of a Cantor set. This measure enables us to provide a geometric interpretation of the Riemann-Liouville's integral of order αϵ├]0,1], and based on this interpretation, the author introduces a modification on the Riemann-Liouville's integral to make it symmetrical and then introduces a new fractional derivative that exploits at the same time the right and the left fractional derivatives.
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