Solutions of semi-linear stochastic evolution integro-differential inclusions with Poisson jumps and non-local initial conditions

Stochastics ◽  
2021 ◽  
pp. 1-33
Author(s):  
Yong-Kui Chang ◽  
Xiaojing Liu ◽  
Zhi-Han Zhao
Keyword(s):  
Differential Inclusions ◽  
Initial Conditions ◽  
Stochastic Evolution ◽  
Poisson Jumps ◽  
Non Local

scholarly journals Asymptotic Stability of Nonlinear Discrete Fractional Pantograph Equations with Non-Local Initial Conditions

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 473
Author(s):  
Jehad Alzabut ◽  
A. George Maria Selvam ◽  
Rami Ahmad El-Nabulsi ◽  
D. Vignesh ◽  
Mohammad Esmael Samei
Keyword(s):  
Fixed Point ◽  
Asymptotic Stability ◽  
Fixed Point Theorems ◽  
Initial Conditions ◽  
Current Collector ◽  
Stability Of Solutions ◽  
Electric Bus ◽  
Pantograph Equation ◽  
Non Local

Pantograph, the technological successor of trolley poles, is an overhead current collector of electric bus, electric trains, and trams. In this work, we consider the discrete fractional pantograph equation of the form Δ*β[k](t)=wt+β,k(t+β),k(λ(t+β)), with condition k(0)=p[k] for t∈N1−β, 0<β≤1, λ∈(0,1) and investigate the properties of asymptotic stability of solutions. We will prove the main results by the aid of Krasnoselskii’s and generalized Banach fixed point theorems. Examples involving algorithms and illustrated graphs are presented to demonstrate the validity of our theoretical findings.

scholarly journals Chimera states and the interplay between initial conditions and non-local coupling

2017 ◽  
Vol 27 (3) ◽  
pp. 033110 ◽  
Author(s):  
Peter Kalle ◽  
Jakub Sawicki ◽  
Anna Zakharova ◽  
Eckehard Schöll
Keyword(s):  
Initial Conditions ◽  
Chimera States ◽  
Non Local ◽  
Local Coupling

Development and Calculation of a Computer Model and Modern Distributed Algorithms for Dispersed Systems Aggregation

2020 ◽  
Vol 11 (2) ◽  
pp. 56-68
Author(s):  
Nurlybek Zhumatayev ◽  
Zhanat Umarova ◽  
Gani Besbayev ◽  
Almira Zholshiyeva
Keyword(s):  
Distributed Algorithms ◽  
Computer Model ◽  
Initial Conditions ◽  
Relaxation Times ◽  
Calculation Algorithm ◽  
Dispersed Systems ◽  
Perfect Model ◽  
Aggregation Processes ◽  
Non Local ◽  
Non Local Equations

In this work, an attempt has been made to eliminate the contradiction of the Smoluchowski equation, using modern distributed algorithms for creating calculation algorithm and implementation a program for building a more perfect model by changing the type of the kinetic equation of aggregation taking into account the relaxation times. On the basis of the applied Mathcad package, there is a developed computer model for calculating the aggregation of dispersed systems. The obtained system of differential equations of the second order is solved by the Runge-Kutt method. The authors are presetting the initial conditions of the calculation. A subsequent analysis was made of the obtained non-local equations and the study of the behavior of solutions of different orders. Also, this research can be aimed at the generalization of the proposed approach for the analysis of aggregation processes in heterogeneous dispersed systems, involving the creation of aggregation models, taking into account both time and space non-locality.

Burgers' equation by non-local shot noise data

1994 ◽  
Vol 31 (A) ◽  
pp. 351-362 ◽  
Author(s):  
Donatas Surgailis ◽  
Wojbor A. Woyczynski
Keyword(s):  
Shot Noise ◽  
Random Fields ◽  
Burgers Equation ◽  
Initial Conditions ◽  
Scaling Limit ◽  
Linear Partial Differential Equation ◽  
Local Case ◽  
Non Linear ◽  
Noise Data ◽  
Non Local

We study the scaling limit of random fields which are solutions of a non-linear partial differential equation, known as the Burgers equation, under stochastic initial conditions. These are assumed to be of a non-local shot noise type and driven by a Cox process. Previous work by Bulinskii and Molchanov (1991), Surgailis and Woyczynski (1993a), and Funaki et al. (1994) concentrated on the case of local shot noise data which permitted use of techniques from the theory of random fields with finite range dependence. Those are not available for the non-local case being considered in this paper.Burgers' equation is known to describe various physical phenomena such as non-linear and shock waves, distribution of self-gravitating matter in the universe, and other flow satisfying conservation laws (see e.g. Woyczynski (1993)).

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