Abstract
We study systems of fractional order differential equations involving the Prabhakar derivative of Caputo type. For commensurate systems we obtain their solutions in closed forms using the eigenvevtors and the eigenvalues of the associated square matrix in the system. We discuss the solutions under the cases where the eigenvalues are distinct, repeated or complex. We present several examples to illustrate the efficiency of the obtained results. For incommensurate systems we apply the Laplace transform to obtain their solutions. As the Prabhakar kernels involve many fractional kernels as particular cases, the obtained results will generalize several existing results in the literature.
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