Abstract
The asymptotic expansions of the Wright functions of the second kind, introduced by Mainardi [see Appendix F of his book Fractional Calculus and Waves in Linear Viscoelasticity (2010)],
Fσ(x)=◀∑▶,Mσ(x)=∞∑n=0(−x)n/n!Γ(−nσ+1−σ) (0<σ<1)
for x → ± ∞ are presented. The situation corresponding to the limit σ → 1− is considered, where Mσ(x) approaches the Dirac delta function δ(x − 1). Numerical results are given to demonstrate the accuracy of the expansions derived in the paper, together with graphical illustrations that reveal the transition to a Dirac delta function as σ → 1−.
Original language | English |
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Pages (from-to) | 54-72 |
Number of pages | 19 |
Journal | Fractional Calculus and Applied Analysis |
Volume | 24 |
Issue number | 1 |
Early online date | 29 Jan 2021 |
DOIs | |
Publication status | Published - 23 Feb 2021 |
Keywords
- Wright function
- Auxiliary Wright function
- Asymptotic expansions
- Exponentially small expansions