scholarly journals Analytical and numerical treatment of a fractional integro-differential equation of volterra-type

1997 ◽  
Vol 25 (12) ◽  
pp. 1-9 ◽  
Author(s):  
L. Boyadjiev ◽  
S.L. Kalla ◽  
H.G. Khajah
Keyword(s):  
Differential Equation ◽  
Numerical Treatment ◽  
Volterra Type ◽  
Integro Differential Equation

scholarly journals A fractional integro-differential equation of volterra type

1998 ◽  
Vol 28 (10) ◽  
pp. 103-113 ◽  
Author(s):  
L. Boyadjiev ◽  
H.-J. Dobner ◽  
S.L. Kalla
Keyword(s):  
Differential Equation ◽  
Volterra Type ◽  
Integro Differential Equation

scholarly journals Fox H-Functions in Self-Consistent Description of a Free-Electron Laser

2021 ◽  
Vol 5 (4) ◽  
pp. 263
Author(s):  
Alexander Iomin
Keyword(s):  
Differential Equation ◽  
Fractional Calculus ◽  
Free Electron ◽  
Free Electron Laser ◽  
High Gain ◽  
The Self ◽  
Volterra Type ◽  
Integro Differential Equation ◽  
Consistent Description ◽  
Self Consistent

A fractional calculus concept is considered in the framework of a Volterra type integro-differential equation, which is employed for the self-consistent description of the high-gain free-electron laser (FEL). It is shown that the Fox H-function is the Laplace image of the kernel of the integro-differential equation, which is also known as a fractional FEL equation with Caputo–Fabrizio type fractional derivative. Asymptotic solutions of the equation are analyzed as well.

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