Abstract
The Mittag–Leffler function (MLF) plays an important role in many applications of fractional calculus, establishing a connection between exponential and power law behaviors that characterize integer and fractional order phenomena, respectively. Nevertheless, the numerical computation of the MLF poses problems both of accuracy and convergence. In this paper, we study the calculation of the 2-parameter MLF by using polynomial computation and integral formulas. For the particular cases having Laplace transform (LT) the method relies on the inversion of the LT using the fast Fourier transform. Experiments with two other available methods compare also the computational time and accuracy. The 3-parameter MLF and its calculation are also considered.
Acknowledgements
This work was funded by Portuguese National Funds through the FCT - Foundation for Science and Technology under the project PEst-UID/EEA/00066/2013.
References
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© 2019 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Research article
- Improved Results on Adaptive Control Approach for Projective Synchronization of Neural Networks with Time-Varying Delay
- A Method to Solve the Reaction-Diffusion-Chemotaxis System
- Two-Phase Flow of Fluid-Particle Interaction over a Stretching Sheet in the Presence of Magnetic Field
- An Algorithm for the Approximate Solution of the Fractional Riccati Differential Equation
- Additional Extension of the Mathematical Model for BCG Immunotherapy of Bladder Cancer and Its Validation by Auxiliary Tool
- Extended Transformed Rational Function Method to Nonlinear Evolution Equations
- Approximation of p-Biharmonic Problem using WEB-Spline based Mesh-Free Method
- Lie Symmetries, One-Dimensional Optimal System and Group Invariant Solutions for the Ripa System
- On the Numerical Computation of the Mittag–Leffler Function
Articles in the same Issue
- Frontmatter
- Research article
- Improved Results on Adaptive Control Approach for Projective Synchronization of Neural Networks with Time-Varying Delay
- A Method to Solve the Reaction-Diffusion-Chemotaxis System
- Two-Phase Flow of Fluid-Particle Interaction over a Stretching Sheet in the Presence of Magnetic Field
- An Algorithm for the Approximate Solution of the Fractional Riccati Differential Equation
- Additional Extension of the Mathematical Model for BCG Immunotherapy of Bladder Cancer and Its Validation by Auxiliary Tool
- Extended Transformed Rational Function Method to Nonlinear Evolution Equations
- Approximation of p-Biharmonic Problem using WEB-Spline based Mesh-Free Method
- Lie Symmetries, One-Dimensional Optimal System and Group Invariant Solutions for the Ripa System
- On the Numerical Computation of the Mittag–Leffler Function