On a new type of fractional difference operators on h-step isolated time scales
Weighted fractional difference operators
Keywords:weighted fractional sum, weighted fractional difference, Caputo fractional weighted difference, Q-operator, Leibniz rule, isolated time scale, integration by parts, nabla discrete Mittag-Leffler function, 2010 MSC: 34A08, 26A33, 39A12
AbstractIn this article, a new type of fractional sums and differences called the discrete weighted fractional
operators are presented. The weighted backward and forward difference operators are defined on an
isolated time scale with arbitrary step size and they obey the power law.
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