Abstract
In this paper we introduce a new ∝-Laplace transform which is a generalization of nabla version of Laplace transform on time scales. In particular for 0< ∝< 1 this transform will serve as fractional Laplace transform on time scales. Existence theorem and some important properties such as linearity, initial and nal value theorem, transform of integral, shifting theorem, transform of derivative are proved. Additionally convolution theorem and formulae for fractional integral, Riemann-Liouville fractional derivative, Liouville-Caputo fractional derivative, Mittag Leer function are given. At last for a suitable value of a fractional dynamic equation with given initial condition is solved.
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