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

A new technique for solving Sobolev type fractional multi-order evolution equations