On a Stochastic Integro-Differential Equation of Volterra Type

1972 ◽  
Vol 23 (4) ◽  
pp. 499-512 ◽  
Author(s):  
W. J. Padgett ◽  
Chris P. Tsokos
Keyword(s):  
Differential Equation ◽  
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.

scholarly journals ON SPECIFIC ASYMPTOTIC STABILITY SOLUTIONS OF A LINEAR HOMOGENEOUS WELTERER INTEGRO-DIFFERENTIAL EQUATION OF THE FOURTH ORDER

2021 ◽  
pp. 110-117
Author(s):  
Z. A. Japarova
Keyword(s):  
Differential Equation ◽  
Asymptotic Stability ◽  
Fourth Order ◽  
Order Differential Equation ◽  
Sufficient Conditions ◽  
Third Order ◽  
Volterra Type ◽  
Integro Differential Equation ◽  
The Third ◽  
Fourth Order Differential Equation

Specific sufficient conditions for the asymptotic stability of a linear homogeneous fourthorder integro-differential equation of the Volterra type are established in the case when all nonzero solutions of the corresponding fourth-order differential equation do not have the property of asymptotic stability of the solutions. In this paper, we obtain estimates on the semiaxis of the solution and the derivative up to the third order.

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