The Prabhakar or three parameter Mittag-Leffler function of a matrix A ∈ ℜ n×n is shown to play a key role in the analysis of visco-elastic systems.The matrix A is allowed to be defective; and for which two methods are presented for the evaluation of the function.One is the spectral method; the second is the Cayley-Hamilton theorem which does not need a knowledge of the eigenvectors.An engineering application is presented by obtaining the solution of a viscoelastic Burgers model.Some strict bounds for the Mittag-Leffler function are also obtained under perturbations of the matrix A.
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Sarah A. Deif (2024) studied this question.
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