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Global Padé Approximations of the Generalized Mittag-Leffler Function and its Inverse by Caibin Zeng; Yang Quan Chen is a Mathematics article available to read on EtoBox.

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This paper proposes a global Padé approximation of the generalized Mittag-Leffler function E α,β (-x) with x ∈ [0, +∞). This uniform approximation can account for both the Taylor series for small arguments and asymptotic series for large arguments. Based on the complete monotonicity of the function E α,β (-x), we work out the global Padé approximation [1/2] for the particular cases {0 < α α}, {0 < α = β 1}, respectively. Moreover, these approximations are inverted to yield a global Padé approximation of the inverse generalized Mittag-Leffler function -L α,β (x) with x ∈ (0, 1/Γ(β)]. We also provide several examples with selected values α and β to compute the relative error from the approximations. Finally, we point out the possible applications using our established approximations in the ordinary and partial time-fractional differential equations in the sense of Riemann-Liouville.

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Author

Caibin Zeng; Yang Quan Chen

Publisher

Springer Science and Business Media LLC

Published

2015

Language

EN

Field

Mathematics (Physical Sciences)