Note on weakly fractional differential equations

Michal Fečkan, Michal Pospíšil, JinRong Wang
2019 Advances in Difference Equations  
In this paper, we compare solutions of q-order fractional differential equations of Caputo type for q near 1 with solutions of the corresponding 1-order ordinary differential equations. By establishing the explicit lower and upper bounds of Mittag-Leffler functions, we obtain the effective convergence results. It is shown that the limit cases q → 1 + and q → 1 -are different. A simple illustrative example is also presented.
doi:10.1186/s13662-019-2086-4 fatcat:zcaqy3filjanbbmtmx43qkvbo4