generalized cauchy problem
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On the Generalized Cauchy Problem for One Class of Differential Equations of Infinite Order

2020 ◽  
Vol 72 (7) ◽  
pp. 1030-1050
Author(s):  
V. V. Horodets’kyi ◽  
O. V. Martynyuk ◽  
R. I. Petryshyn
Keyword(s):  
Cauchy Problem ◽  
Differential Equations ◽  
Infinite Order ◽  
Generalized Cauchy Problem

scholarly journals Space–time fractional Zener wave equation

2015 ◽  
Vol 471 (2174) ◽  
pp. 20140614 ◽  
Author(s):  
T.M. Atanackovic ◽  
M. Janev ◽  
Lj. Oparnica ◽  
S. Pilipovic ◽  
D. Zorica
Keyword(s):  
Wave Equation ◽  
Space Time ◽  
Strain Measure ◽  
Zener Model ◽  
Numerical Examples ◽  
Finite Speed ◽  
Special Cases ◽  
Uniqueness Of The Solution ◽  
Fractional Zener Model ◽  
Generalized Cauchy Problem

The space–time fractional Zener wave equation, describing viscoelastic materials obeying the time-fractional Zener model and the space-fractional strain measure, is derived and analysed. This model includes waves with finite speed, as well as non-propagating disturbances. The existence and the uniqueness of the solution to the generalized Cauchy problem are proved. Special cases are investigated and numerical examples are presented.

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