scholarly journals Solutions for impulsive fractional pantograph differential equation via generalized anti-periodic boundary condition

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Idris Ahmed ◽  
Poom Kumam ◽  
Jamilu Abubakar ◽  
Piyachat Borisut ◽  
Kanokwan Sitthithakerngkiet
Keyword(s):  
Differential Equation ◽  
Boundary Condition ◽  
Fixed Point ◽  
Fractional Differential Equation ◽  
Existence And Uniqueness ◽  
Periodic Boundary Condition ◽  
Periodic Boundary ◽  
Fixed Point Theorems ◽  
Uniqueness Of The Solution ◽  
Fractional Differential

Abstract This study investigates the solutions of an impulsive fractional differential equation incorporated with a pantograph. This work extends and improves some results of the impulsive fractional differential equation. A differential equation of an impulsive fractional pantograph with a more general anti-periodic boundary condition is proposed. By employing the well-known fixed point theorems of Banach and Krasnoselskii, the existence and uniqueness of the solution of the proposed problem are established. Furthermore, two examples are presented to support our theoretical analysis.

Optically Derived Signal Set For Phased Array Antennas

1987 ◽  
Author(s):  
M. G. Parent ◽  
L. Goldberg ◽  
P. D. Stilwell, Jr.
Keyword(s):  
Phased Array ◽  
Phased Array Antennas ◽  
Signal Set ◽  
Array Antennas

scholarly journals A new time-delayed periodic boundary condition for discrete element modelling of railway track under moving wheel loads

2021 ◽  
Vol 23 (4) ◽  
Author(s):  
Huiqi Li ◽  
Glenn McDowell ◽  
John de Bono
Keyword(s):  
Boundary Condition ◽  
Periodic Boundary Condition ◽  
Periodic Boundary ◽  
Discrete Element ◽  
Contact Forces ◽  
Railway Track ◽  
Discrete Element Modelling ◽  
Fixed Boundary ◽  
Element Modelling ◽  
New Time

Abstract A new time-delayed periodic boundary condition (PBC) has been proposed for discrete element modelling (DEM) of periodic structures subject to moving loads such as railway track based on a box test which is normally used as an element testing model. The new proposed time-delayed PBC is approached by predicting forces acting on ghost particles with the consideration of different loading phases for adjacent sleepers whereas a normal PBC simply gives the ghost particles the same contact forces as the original particles. By comparing the sleeper in a single sleeper test with a fixed boundary, a normal periodic boundary and the newly proposed time-delayed PBC (TDPBC), the new TDPBC was found to produce the closest settlement to that of the middle sleeper in a three-sleeper test which was assumed to be free of boundary effects. It appears that the new TDPBC can eliminate the boundary effect more effectively than either a fixed boundary or a normal periodic cell. Graphic abstract

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