Abstract.

Multi-term fractional diferential equations have been studied because of their ap plications in modelling, and solved using miscellaneous mathematical methods. We present explicit analytical solutions for several families of generalized multidimensional Bagley-Torvik equations with permutable matrices and two various fractional orders which are satisfying both homogeneous and inhomogeneous cases. The results are obtained by means of Mittag-Leffler type matrix functions with double innite series.

Keywords:

Bagley-Torvik equations, Caputo fractional diferentiation, Mittag-Leffler type func- tions, Fox-Wright functions, double innite series.