On Mittag-Leffler-type functions in fractional evolution processes
Journal of Computational and Applied Mathematics - Special issue on higher transcendental functions and their applications
On the numerical inversion of the Laplace transform of certain holomorphic mappings
Applied Numerical Mathematics
Theory and Applications of Fractional Differential Equations, Volume 204 (North-Holland Mathematics Studies)
A Spectral Order Method for Inverting Sectorial Laplace Transforms
SIAM Journal on Numerical Analysis
Numerical Methods for Special Functions
Numerical Methods for Special Functions
Numerical Algorithm for Calculating the Generalized Mittag-Leffler Function
SIAM Journal on Numerical Analysis
On accurate product integration rules for linear fractional differential equations
Journal of Computational and Applied Mathematics
On the use of matrix functions for fractional partial differential equations
Mathematics and Computers in Simulation
Generalized exponential time differencing methods for fractional order problems
Computers & Mathematics with Applications
A Contour Integral Method for the Black-Scholes and Heston Equations
SIAM Journal on Scientific Computing
On the Convergence of Krylov Subspace Methods for Matrix Mittag-Leffler Functions
SIAM Journal on Numerical Analysis
A family of Adams exponential integrators for fractional linear systems
Computers & Mathematics with Applications
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This paper addresses the problem of the numerical computation of generalized Mittag---Leffler functions with two parameters, with applications in fractional calculus. The inversion of their Laplace transform is an effective tool in this direction; however, the choice of the integration contour is crucial. Here parabolic contours are investigated and combined with quadrature rules for the numerical integration. An in-depth error analysis is carried out to select suitable contour's parameters, depending on the parameters of the Mittag---Leffler function, in order to achieve any fixed accuracy. We present numerical experiments to validate theoretical results and some computational issues are discussed.