A new characteristic property of Mittag-Leffler functions and fractional cosine functions

• Autorzy: Zhan-Dong Mei , Ji-Gen Peng , Jun-Xiong Jia
• Języki publikacji: EN

Abstrakty

EN

A new characteristic property of the Mittag-Leffler function $E_{α}(at^{α})$ with 1 < α < 2 is deduced. Motivated by this property, a new notion, named α-order cosine function, is developed. It is proved that an α-order cosine function is associated with a solution operator of an α-order abstract Cauchy problem. Consequently, an α-order abstract Cauchy problem is well-posed if and only if its coefficient operator generates a unique α-order cosine function.

Kategorie tematyczne

• 47D09: Operator sine and cosine functions and higher-order Cauchy problems
• 45N05: Abstract integral equations, integral equations in abstract spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2014
• Tom: 220
• Numer: 2
• Strony: 119-140

Daty

wydano

2014

Twórcy

autor

Zhan-Dong Mei

• School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, China

autor

Ji-Gen Peng

• School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, China

autor

Jun-Xiong Jia

• School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, China

Identyfikatory

DOI

10.4064/sm220-2-2