  A strong inspiration for studying Sobolev type fractional evolution equations
comes from the fact that have been verified to be useful tools in the modeling
of many physical processes. We introduce a novel technique for solving Sobolev
type fractional evolution equations with multi-orders in a Banach space. We
propose a new Mittag-Leffler type function which is generated by linear bounded
operators and investigate their properties which are productive for checking
the candidate solutions for multi-term fractional differential equations.
Furthermore, we propose an exact analytical representation of solutions for
multi-dimensional fractional-order dynamical systems with nonpermutable and
permutable matrices.
