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In this paper, our formulation generalizes the fractional power series to the matrix form and a new version of the matrix fractional Taylor’s series is also considered in terms of Caputo’s fractional derivative. Moreover, several significant results have been realignment to these generalizations. Finally, to demonstrate the capability and efficiency of our theoretical results, we present the solutions of three linear non-homogenous higher order ( m  − 1 &lt;  α  ≤  m ,  m  ∈  N ) matrix fractional differential equations by using our new approach.

A class of linear non-homogenous higher order matrix fractional differential equations: Analytical solutions and new technique