THE GENERALIZED MITTAG-LEFFLER FUNCTION
OF MATRIX ARGUMENT AND THE MODELING
OF A VISCO-ELASTIC SYSTEM

Sarah A. Deif
Department of Engineering Mathematics
Cairo University, Giza 12316, EGYPT

Abstract


Abstract. The Prabhakar or three parameter Mittag-Leffler function of a matrix ${\rm\; }A\in \Re ^{n\times n} $ is shown to play a key role in the analysis of visco-elastic systems. The matrix $\textit{A}$ 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 $A$.

Received: 30 Oct. 2023

AMS Subject Classification: 33E12; 34A08; 15A16

Key Words and Phrases: fractional differential equations; Caputo derivative; Mittag-Leffler functions; Cayley-Hamilton theorem, the Burgers model, error bounds

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How to cite this paper?
DOI: 10.12732/ijam.v36i6.8
Source: International Journal of Applied Mathematics
ISSN printed version: 1311-1728
ISSN on-line version: 1314-8060
Year: 2023
Volume: 36
Issue: 6
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