Fractional Calculus on Time Scales
by Paul Williams
Abstract: Time scales calculus is a relatively new field of analysis
with the goal of unifying discreet and continuum forms of calculus. It
considers functions whose domain is a closed subset of the real
numbers, and a “derivative” with the property that if the domain was
all of the real numbers it is consistent with the normal derivative.
But when the domain is the integers it is consistent with the
difference operator seen in discrete analysis.
Fractional calculus is the study of non-integer orders of integration
and differentiation. In recent work the study of non-integer orders of
the difference operators has gained momentum. This talk will
investigate the open problem of defining fractional calculus on time
scales, such that it unifies the definitions in the literature. No
prior knowledge of time scales calculus or fractional calculus will be
assumed in the talk.
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