scholarly journals Existence and Stability Analysis for Fractional Impulsive Caputo Difference-Sum Equations with Periodic Boundary Condition

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 843 ◽  
Author(s):  
Rujira Ouncharoen ◽  
Saowaluck Chasreechai ◽  
Thanin Sitthiwirattham
Keyword(s):  
Boundary Condition ◽  
Fixed Point ◽  
Periodic Boundary Condition ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Existence Results ◽  
Ulam Stability ◽  
Banach Contraction ◽  
Existence And Stability ◽  
The Banach Contraction Principle

In this paper, by using the Banach contraction principle and the Schauder’s fixed point theorem, we investigate existence results for a fractional impulsive sum-difference equations with periodic boundary conditions. Moreover, we also establish different kinds of Ulam stability for this problem. An example is also constructed to demonstrate the importance of these results.

Existence Results of Mild Solutions for Impulsive Fractional Evolution Equations with Periodic Boundary Condition

2017 ◽  
Vol 18 (7-8) ◽  
pp. 585-598
Author(s):  
Baolin Li ◽  
Haide Gou
Keyword(s):  
Boundary Condition ◽  
Fixed Point ◽  
Periodic Boundary Condition ◽  
Periodic Boundary ◽  
Fixed Point Theorems ◽  
Evolution Equations ◽  
Existence Theorems ◽  
Mild Solutions ◽  
Existence Results ◽  
Fractional Evolution Equations

AbstractThis paper discusses the existence of mild solutions for a class of fractional impulsive evolution equation with periodic boundary condition and noncompact semigroup. By using some fixed-point theorems, the existence theorems of mild solutions are obtained, our results are also more general than known results. Furthermore, as an application that illustrates the abstract results, two examples are given.

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.

scholarly journals Existence results for fractional neutral integro-differential systems with nonlocal condition through resolvent operators

2019 ◽  
Vol 27 (1) ◽  
pp. 107-124
Author(s):  
D. Mallika ◽  
D. Baleanu ◽  
S. Suganya ◽  
M. Mallika Arjunan
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Nonlocal Condition ◽  
Nonlocal Conditions ◽  
Existence Results ◽  
Resolvent Operators ◽  
Differential Systems ◽  
Banach Contraction ◽  
Krasnoselskii Fixed Point Theorem ◽  
The Banach Contraction Principle

Abstract The manuscript is primarily concerned with the new existence results for fractional neutral integro-differential equation (FNIDE) with nonlocal conditions (NLCs) in Banach spaces. Based on the Banach contraction principle and Krasnoselskii fixed point theorem (FPT) joined with resolvent operators, we develop the main results. Ultimately, an representation is also offered to demonstrate the accomplished theorem.

scholarly journals Computation of Flutter of Turbomachinery Cascades Using a Parallel Unsteady Navier-Stokes Code

1998 ◽  
Author(s):  
Shanhong Ji ◽  
Feng Liu
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Periodic Boundary Condition ◽  
Periodic Boundary ◽  
Unsteady Flows ◽  
Periodic Boundary Conditions ◽  
Navier Stokes ◽  
Compressor Cascade ◽  
Multiple Passage ◽  
Parallel Code

A quasi-three-dimensional multigrid Navier-Stokes solver on single and multiple passage domains is presented for solving unsteady flows around oscillating turbine and compressor blades. The conventional “direct store” method is used for applying the phase-shifted periodic boundary condition over a single blade passage. A parallel version of the solver using the Message Passing Interface (MPI) standard is developed for multiple passage computations. In the parallel multiple passage computations, the phase-shifted periodic boundary condition is converted to simple in-phase periodic condition. Euler and Navier-Stokes solutions are obtained for unsteady flows through an oscillating turbine cascade blade row with both the sequential and the parallel code. It is found that the parallel code offers almost linear speedup with multiple CPUs. In addition, significant improvement is achieved in convergence of the computation to a periodic unsteady state in the parallel multiple passage computations due to the use of in-phase periodic boundary conditions as compared to that in the single passage computations with phase-lagged periodic boundary conditions via the “direct store” method. The parallel Navier-Stokes code is also used to calculate the flow through an oscillating compressor cascade. Results are compared with experimental data and computations by other authors.

A PENALTY METHOD FOR SOLVING PARTIAL DIFFERENTIAL EQUATIONS WITH PERIODIC BOUNDARY CONDITION: APPLICATION TO THE HOMOGENIZATION THEORY

1998 ◽  
Vol 08 (05) ◽  
pp. 749-760 ◽  
Author(s):  
BOUJEMAA AOUBIZA ◽  
MOHAMED RACHID LAYDI
Keyword(s):  
Boundary Condition ◽  
Error Estimate ◽  
Elliptic Problem ◽  
Penalty Method ◽  
Periodic Boundary Condition ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Homogenization Theory ◽  
Numerical Tests ◽  
Penalization Technique

We present a numerical method, based on a penalization technique, for the solution of an elliptic problem with periodic boundary conditions. The convergence of the method is established and an error estimate is given. Numerical tests are performed on some problems from homogenization theory.

A generalization of Reich’s fixed point theorem for multi-valued mappings

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3295-3305 ◽  
Author(s):  
Antonella Nastasi ◽  
Pasquale Vetro
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contractive Condition ◽  
Complete Metric Spaces ◽  
New Class ◽  
Banach Contraction ◽  
The Banach Contraction Principle

Motivated by a problem concerning multi-valued mappings posed by Reich [S. Reich, Some fixed point problems, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 57 (1974) 194-198] and a paper of Jleli and Samet [M. Jleli, B. Samet, A new generalization of the Banach contraction principle, J. Inequal. Appl. 2014:38 (2014) 1-8], we consider a new class of multi-valued mappings that satisfy a ?-contractive condition in complete metric spaces and prove some fixed point theorems. These results generalize Reich?s and Mizoguchi-Takahashi?s fixed point theorems. Some examples are given to show the usability of the obtained results.

scholarly journals On the Nonlocal Fractional Delta-Nabla Sum Boundary Value Problem for Sequential Fractional Delta-Nabla Sum-Difference Equations

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 476
Author(s):  
Jiraporn Reunsumrit ◽  
Thanin Sitthiwirattham
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Difference Equations ◽  
Existence And Uniqueness ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Banach Contraction ◽  
The Banach Contraction Principle

In this paper, we propose sequential fractional delta-nabla sum-difference equations with nonlocal fractional delta-nabla sum boundary conditions. The Banach contraction principle and the Schauder’s fixed point theorem are used to prove the existence and uniqueness results of the problem. The different orders in one fractional delta differences, one fractional nabla differences, two fractional delta sum, and two fractional nabla sum are considered. Finally, we present an illustrative example.

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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