TY - JOUR AU - Kisela, Tomáš PY - 2013 DA - 2013/08/23 TI - Power functions and essentials of fractional calculus on isolated time scales JO - Advances in Difference Equations SP - 259 VL - 2013 IS - 1 AB - This paper is concerned about a recently suggested axiomatic definition of power functions on a general time scale and its consequences to fractional calculus. Besides a discussion of the existence and uniqueness of such functions, we derive an efficient formula for the computation of power functions of rational orders on an arbitrary isolated time scale. It can be utilized in the introduction and evaluation of fractional sums and differences. We also deal with the Laplace transform of such fractional operators, which, apart from solving of fractional difference equations, enables a more detailed comparison of our results with those in the relevant literature. Some illustrating examples (including special fractional initial value problems) are presented as well. SN - 1687-1847 UR - https://doi.org/10.1186/1687-1847-2013-259 DO - 10.1186/1687-1847-2013-259 ID - Kisela2013 ER -