Existence of solutions for k‐dimensional system of multi‐term fractional q‐integro‐differential equations under anti‐periodic boundary conditions via quantum calculus

2020 ◽  
Author(s):  
Mohammad Esmael Samei ◽  
Wengui Yang
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Periodic Boundary ◽  
Existence Of Solutions ◽  
Periodic Boundary Conditions ◽  
Dimensional System ◽  
Quantum Calculus

scholarly journals The existence of solution for a k-dimensional system of fractional differential inclusions with anti-periodic boundary value conditions

Filomat ◽  
2016 ◽  
Vol 30 (6) ◽  
pp. 1601-1613 ◽  
Author(s):  
Vahid Hedayati ◽  
Shahram Rezapour
Keyword(s):  
Boundary Conditions ◽  
Differential Inclusions ◽  
Periodic Boundary ◽  
Existence Of Solutions ◽  
Periodic Boundary Conditions ◽  
Existence Of Solution ◽  
Inclusion Problem ◽  
Dimensional System ◽  
Fractional Differential Inclusions ◽  
Fractional Differential

We investigate the existence of solutions for a k-dimensional systems of fractional differential inclusions with anti-periodic boundary conditions. We provide two results via different conditions for obtaining solutions of the k-dimensional inclusion problem. We provide some examples to illustrate our results.

One-Dimensional Unsteady Periodic Flow Model with Boundary Conditions Constrained by Differential Equations

2009 ◽  
Vol 131 (6) ◽  
Author(s):  
Nhan T. Nguyen
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Euler Equations ◽  
Periodic Boundary ◽  
Closed Loop ◽  
Fluid Transport ◽  
Periodic Boundary Conditions ◽  
Transport Systems ◽  
Variable Approach ◽  
Upwind Method

This paper describes a modeling method for closed-loop unsteady fluid transport systems based on 1D unsteady Euler equations with nonlinear forced periodic boundary conditions. A significant feature of this model is the incorporation of dynamic constraints on the variables that control the transport process at the system boundaries as they often exist in many transport systems. These constraints result in a coupling of the Euler equations with a system of ordinary differential equations that model the dynamics of auxiliary processes connected to the transport system. Another important feature of the transport model is the use of a quasilinear form instead of the flux-conserved form. This form lends itself to modeling with measurable conserved fluid transport variables and represents an intermediate model between the primitive variable approach and the conserved variable approach. A wave-splitting finite-difference upwind method is presented as a numerical solution of the model. An iterative procedure is implemented to solve the nonlinear forced periodic boundary conditions prior to the time-marching procedure for the upwind method. A shock fitting method to handle transonic flow for the quasilinear form of the Euler equations is presented. A closed-loop wind tunnel is used for demonstration of the accuracy of this modeling method.

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