Power functions and essentials of fractional calculus on isolated time scales

被引:0
作者
Tomáš Kisela
机构
[1] Brno University of Technology,Institute of Mathematics
来源
Advances in Difference Equations | / 2013卷
关键词
fractional calculus; power functions; time scales; convolution; Laplace transform;
D O I
暂无
中图分类号
学科分类号
摘要
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.
引用
收藏
相关论文
共 20 条
  • [1] Agarwal RP(1969)Certain fractional Math. Proc. Camb. Philos. Soc 66 365-370
  • [2] Diaz R(1974)-integrals and Math. Comput 28 185-202
  • [3] Osler TJ(2010)-derivatives J. Nonlinear Math. Phys 17 51-68
  • [4] Čermák J(2012)Differences of fractional order Fract. Calc. Appl. Anal 15 616-638
  • [5] Nechvátal L(2007)On Int. J. Differ. Equ 2 165-176
  • [6] Williams PA(2009)-analogue of fractional calculus Fract. Calc. Appl. Anal 12 159-178
  • [7] Atici FM(2003)Fractional calculus on time scales with Taylor’s theorem J. Nonlinear Math. Phys 10 133-142
  • [8] Eloe PW(2011)A transform method in discrete fractional calculus Comput. Math. Appl 62 1790-1797
  • [9] Mansour ZSI(2013)Linear sequential Appl. Math. Comput 219 7012-7022
  • [10] Nagai A(2010)-difference equations of fractional order Comput. Math. Appl 59 3750-3762