On the analysis of mixed-index time fractional differential equation systems

نویسندگان

  • Kevin Burrage
  • Pamela Burrage
  • Ian Turner
  • Fanhai Zeng
چکیده

In this paper we study the class of mixed-index time fractional differential equations in 1 which different components of the problem have different time fractional derivatives on the left hand 2 side. We prove a theorem on the solution of the linear system of equations, which collapses to the 3 well-known Mittag-Leffler solution in the case the indices are the same, and also generalises the 4 solution of the so-called linear sequential class of time fractional problems. We also investigate the 5 asymptotic stability properties of this class of problems using Laplace transforms and show how 6 Laplace transforms can be used to write solutions as linear combinations of generalised Mittag-Leffler 7 functions in some cases. Finally we illustrate our results with some numerical simulations. 8

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تاریخ انتشار 2018