On fractional Cauchy-type problems containing Hilfer's derivative

Rafał Kamocki, Cezary Obczyński
2016 Electronic Journal of Qualitative Theory of Differential Equations  
In the paper we study fractional systems with generalized Riemann-Liouville derivatives. A theorem on the existence and uniqueness of a solution to a fractional nonlinear ordinary Cauchy problem is proved. Next a formula for the solution to a linear problem of such a type is presented.
doi:10.14232/ejqtde.2016.1.50 fatcat:wd5oy5wi5zfpvoz2bq7qz7si3m