A Filippov's theorem, some existence results and the compactness of solution sets of impulsive fractional order differential inclusions
The authors show an impulsive version of Filippov's theorem and also establish existence results for a fractional differential inclusion of the form \[ D_\ast^\alpha y(t)\in F(t,y(t))\text{ a.e. } t\in [0,b]\backslash\{t_1,\dotsc, t_m\},\;\alpha\in(0,1], \] \[ y(t_k^+)-y(t_k^-)= I_k(y(t_k^-)), \;k=1,\dotsc, m, \] \[ y(0)=a, \] where \(D_\ast^\alpha\) denotes the Caputo fractional derivative, \(F\) is a set-valued map and \(I_k\) are continuous functions.
scientific article; zbMATH DE number 6107822
scientific article