Abstract
Starting from the matrix form of the fractional Cauchy problem, new formulae for the sum of the three-parameter Mittag-Leffler functions are deduced. The derivation is based on the Prabhakar fractional integral operator. A Volterra integral equation relating the solution of the Cauchy problem with that of a perturbed problem is also obtained; from this a condition number measuring the sensitivity of the solution to changes in data can be derived. Several examples are also incorporated to test the bounds.
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