scholarly journals Some Kinds of the Controllable Problems for Fuzzy Control Dynamic Systems

2018 ◽  
Vol 140 (9) ◽  
Author(s):  
N. D. Phu ◽  
P. V. Tri ◽  
A. Ahmadian ◽  
S. Salahshour ◽  
D. Baleanu
Keyword(s):  
Dynamic Systems ◽  
Existence And Uniqueness ◽  
Fuzzy Systems ◽  
Local Existence ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Global Existence And Uniqueness ◽  
Control Dynamic ◽  
Generalized Lipschitz Condition ◽  
Fuzzy Solutions

In this work, we have discussed the fuzzy solutions for fuzzy controllable problem, fuzzy feedback problem, and fuzzy global controllable (GC) problems. We use the method of successive approximations under the generalized Lipschitz condition for the local existence and furthermore, we have described the contraction principle under suitable conditions for global existence and uniqueness of fuzzy solutions. We have too the GC results for fuzzy systems. Some examples and computer simulation illustrating our approach are also given for these controllable problems.

scholarly journals Fuzzy Volterra integral equations with in-finite delay

2009 ◽  
Vol 40 (1) ◽  
pp. 19-29 ◽  
Author(s):  
P. Prakash ◽  
V. Kalaiselvi
Keyword(s):  
Integral Equations ◽  
Existence And Uniqueness ◽  
Infinite Delay ◽  
Volterra Integral Equations ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Uniqueness Of Solutions ◽  
Finite Delay

In this paper, we study the existence and uniqueness of solutions for a class of fuzzy Volterra integral equations with infinite delay by using the method of successive approximations.

scholarly journals Random Fuzzy Differential Equations with Impulses

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Ho Vu
Keyword(s):  
Differential Equations ◽  
Existence And Uniqueness ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Uniqueness Of Solutions ◽  
Picard Method

We consider the random fuzzy differential equations (RFDEs) with impulses. Using Picard method of successive approximations, we shall prove the existence and uniqueness of solutions to RFDEs with impulses under suitable conditions. Some of the properties of solution of RFDEs with impulses are studied. Finally, an example is presented to illustrate the results.

scholarly journals About the existence and uniqueness theorem for hyperbolic equation

1995 ◽  
Vol 18 (1) ◽  
pp. 141-146
Author(s):  
M. E. Khalifa
Keyword(s):  
Hyperbolic Equation ◽  
Uniqueness Theorem ◽  
Existence And Uniqueness ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Existence And Uniqueness Theorem ◽  
Almost Everywhere

In this paper we prove the existence and uniqueness theorem for almost everywhere solution of the hyperbolic equation using the method of successive approximations [1].

scholarly journals Existence and Uniqueness of Fuzzy Control Integro-Differential Equation with Perturbed

2013 ◽  
Vol 3 ◽  
pp. 37-44 ◽  
Author(s):  
N. Phuong ◽  
N.N. Phung ◽  
H. Vu
Keyword(s):  
Differential Equation ◽  
Fuzzy Control ◽  
Integrodifferential Equation ◽  
Existence And Uniqueness ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Integro Differential Equation

In the paper, we discuss the existence and uniqueness solution of fuzzy control integrodifferential equation with perturbed. The method of successive approximations is utilized toestablish these results.

scholarly journals Nonlinear stochastic functional integral equations in the plane

1995 ◽  
Vol 8 (4) ◽  
pp. 371-379 ◽  
Author(s):  
Jan Turo
Keyword(s):  
Global Existence ◽  
Integral Equations ◽  
Existence And Uniqueness ◽  
Functional Integral ◽  
Successive Approximations ◽  
Uniqueness Theorems ◽  
Existence And Uniqueness Theorems ◽  
Global Existence And Uniqueness ◽  
Functional Integral Equations ◽  
Stochastic Functional

Local or global existence and uniqueness theorems for nonlinear stochastic functional integral equations are proved. The proofs are based on the successive approximations methods. The formulation includes retarded arguments and hereditary Volterra terms.

Construction of a unique mild solution of one-dimensional Keller-Segel systems with uniformly elliptic operators having variable coefficients

2018 ◽  
Vol 68 (4) ◽  
pp. 845-866
Author(s):  
Yumi Yahagi
Keyword(s):  
Mild Solution ◽  
Existence And Uniqueness ◽  
Local Existence ◽  
Variable Coefficients ◽  
Elliptic Operators ◽  
Successive Approximations ◽  
Main Method ◽  
One Dimensional ◽  
Local Existence And Uniqueness ◽  
Unique Mild Solution

Abstract A one-dimensional Keller-Segel system which is defined through uniformly elliptic operators having variable coefficients is considered. In the main theorems, the local existence and uniqueness of the mild solution of the system are proved. The main method to construct the mild solution is an argument of successive approximations by means of strongly continuous semi-groups.

scholarly journals The Burgers’ equation with stochastic transport: shock formation, local and global existence of smooth solutions

2019 ◽  
Vol 26 (6) ◽  
Author(s):  
Diego Alonso-Orán ◽  
Aythami Bethencourt de León ◽  
So Takao
Keyword(s):  
Global Existence ◽  
Existence And Uniqueness ◽  
Stochastic Equation ◽  
Burgers Equation ◽  
Blow Up ◽  
Local Existence ◽  
Smooth Solutions ◽  
Local Existence And Uniqueness ◽  
Stochastic Transport ◽  
Global Existence And Uniqueness

Abstract In this work, we examine the solution properties of the Burgers’ equation with stochastic transport. First, we prove results on the formation of shocks in the stochastic equation and then obtain a stochastic Rankine–Hugoniot condition that the shocks satisfy. Next, we establish the local existence and uniqueness of smooth solutions in the inviscid case and construct a blow-up criterion. Finally, in the viscous case, we prove global existence and uniqueness of smooth solutions.

Parametric Excitation Under Multiple Excitation Parameters: Asymmetric Plates Under a Rotating Spring

1991 ◽  
Author(s):  
I. Y. Shen ◽  
C. D. Mote
Keyword(s):  
Dynamic Systems ◽  
Equations Of Motion ◽  
System Stability ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Matrix Eigenvalue Problem ◽  
Secondary Resonances ◽  
Nonlinear Matrix ◽  
Perturbation Parameters ◽  
Floquet Theorem

Abstract A perturbation method is developed to predict stability of parametrically excited dynamic systems containing multiple perturbation parameters. This method, based on the Floquet theorem and the method of successive approximations, results in a nonlinear matrix eigenvalue problem whose eigenvalues are used to predict the system stability. The method is applied to a classical circular plate, containing elastic or viscoelastic inclusions, excited by a linear transverse spring rotating at constant speed. Primary and secondary resonances are predicted. The transition to instability predicted by the perturbation analysis agrees with predictions obtained by numerical integration of the equations of motion.

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