scholarly journals Rotational periodic solutions for fractional iterative systems

2021 ◽  
Vol 6 (10) ◽  
pp. 11233-11245
Author(s):  
Rui Wu ◽  
◽  
Yi Cheng ◽  
Ravi P. Agarwal ◽  
◽  
...  
Keyword(s):  
Existence And Uniqueness ◽  
Nonlinear Term ◽  
Existence Of Solutions ◽  
Degree Theory ◽  
Periodic Problem ◽  
Network System ◽  
Well Posedness ◽  
Topological Degree Theory ◽  
Neural Network System ◽  
Iterative Systems

<abstract><p>In this paper, we devoted to deal with the rotational periodic problem of some fractional iterative systems in the sense of Caputo fractional derivative. Under one sided-Lipschtiz condition on nonlinear term, the existence and uniqueness of solution for a fractional iterative equation is proved by applying the Leray-Schauder fixed point theorem and topological degree theory. Furthermore, the well posedness for a nonlinear control system with iteration term and a multivalued disturbance is established by using set-valued theory. The existence of solutions for a iterative neural network system is demonstrated at the end.</p></abstract>

scholarly journals Dynamic behaviors for inertial neural networks with reaction-diffusion terms and distributed delays

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Famei Zheng
Keyword(s):  
Neural Networks ◽  
Equilibrium Point ◽  
Existence And Uniqueness ◽  
Global Exponential Stability ◽  
Degree Theory ◽  
Reaction Diffusion ◽  
Distributed Delays ◽  
Sufficient Condition ◽  
Topological Degree Theory ◽  
Inertial Neural Networks

AbstractA class of inertial neural networks (INNs) with reaction-diffusion terms and distributed delays is studied. The existence and uniqueness of the equilibrium point for the considered system is obtained by topological degree theory, and a sufficient condition is given to guarantee global exponential stability of the equilibrium point. Finally, an example is given to show the effectiveness of the results in this paper.

scholarly journals Uniqueness and existence of solutions for nonlinear fractional differential equations with two fractional orders

Mathematica ◽  
2021 ◽  
Vol 63 (86) (2) ◽  
pp. 254-267
Author(s):  
Mohamed Houas ◽  
◽  
Zoubir Dahmani ◽  
Erhan Set ◽  
◽  
...  
Keyword(s):  
Differential Equations ◽  
Existence And Uniqueness ◽  
Existence Of Solutions ◽  
Degree Theory ◽  
Uniqueness Of Solutions ◽  
Nonlinear Alternative ◽  
Banach’S Fixed Point Theorem ◽  
Fractional Differential ◽  
Uniqueness And Existence ◽  
Fractional Orders

We study the existence and uniqueness of solutions for integro-differential equations involving two fractional orders. By using the Banach’s fixed point theorem, Leray-Schauder’s nonlinear alternative and Leray-Schauder’s degree theory, the existence and uniqueness of solutions are obtained. Some illustrative examples are also presented.

scholarly journals Solutions of nonlinear integrodifferential equations of mixed type in Banach spaces

1989 ◽  
Vol 2 (1) ◽  
pp. 1-11 ◽  
Author(s):  
Dajun Guo
Keyword(s):  
Mixed Type ◽  
Existence Of Solutions ◽  
Degree Theory ◽  
Monotone Iterative Technique ◽  
Integrodifferential Equations ◽  
Topological Degree Theory ◽  
Initial Value ◽  
Monotone Iterative ◽  
Equations Of Mixed Type ◽  
Minimal And Maximal Solutions

In this paper, the author combines the topological degree theory and the monotone iterative technique to investigate the existence of solutions and also minimal and maximal solutions of the initial value problem for nonlinear integrodifferential equations of mixed type in Banach space. Two main theorems are obtained and two examples are given.

scholarly journals Existence of solutions for a coupled system of fractional differential equations by means of topological degree theory

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Jingli Xie ◽  
Lijing Duan
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Topological Degree ◽  
Existence Of Solutions ◽  
Degree Theory ◽  
Coupled System ◽  
Topological Degree Theory ◽  
Fractional Differential

AbstractThis paper investigates the existence of solutions for a coupled system of fractional differential equations. The existence is proved by using the topological degree theory, and an example is given to show the applicability of our main result.

scholarly journals APPLICABILITY OF TOPOLOGICAL DEGREE THEORY TO EVOLUTION EQUATION WITH PROPORTIONAL DELAY

Fractals ◽  
2020 ◽  
Vol 28 (08) ◽  
pp. 2040028
Author(s):  
MUHAMMAD SHER ◽  
KAMAL SHAH ◽  
YU-MING CHU ◽  
RAHMAT ALI KHAN
Keyword(s):  
Evolution Equation ◽  
Caputo Derivative ◽  
Existence And Uniqueness ◽  
Topological Degree ◽  
Degree Theory ◽  
Proportional Delay ◽  
Ulam Stability ◽  
Topological Degree Theory ◽  
Local Conditions ◽  
Fractional Order Differential Equations

In this paper, we use the topological degree theory (TDT) to investigate the existence and uniqueness of solution for a class of evolution fractional order differential equations (FODEs) with proportional delay using Caputo derivative under local conditions. In the same line, we will also study different kinds of Ulam stability such as Ulam–Hyers (UH) stability, generalized Ulam–Hyers (GUH) stability, Ulam–Hyers–Rassias (UHR) stability and generalized Ulam–Hyers–Rassias (GUHR) stability for the considered problem. To justify our results we provide an example.

scholarly journals Semilinear systems with a multi-valued nonlinear term

2017 ◽  
Vol 15 (1) ◽  
pp. 628-644
Author(s):  
In-Sook Kim ◽  
Suk-Joon Hong
Keyword(s):  
Hilbert Space ◽  
Linear Operator ◽  
Nonlinear Term ◽  
Degree Theory ◽  
Existence Results ◽  
Topological Degree Theory ◽  
Dirichlet Problems ◽  
Semilinear Systems ◽  
Densely Defined ◽  
Monotone Type

Abstract Introducing a topological degree theory, we first establish some existence results for the inclusion h ∈ Lu − Nu in the nonresonance and resonance cases, where L is a closed densely defined linear operator on a Hilbert space with a compact resolvent and N is a nonlinear multi-valued operator of monotone type. Using the nonresonance result, we next show that abstract semilinear system has a solution under certain conditions on N = (N1, N2), provided that L = (L1, L2) satisfies dim Ker L1 = ∞ and dim Ker L2 < ∞. As an application, periodic Dirichlet problems for the system involving the wave operator and a discontinuous nonlinear term are discussed.

On the existence of solutions for singular boundary value problem of third-order differential equations

2010 ◽  
Vol 60 (4) ◽  
Author(s):  
Feng Wang ◽  
Yujun Cui
Keyword(s):  
Differential Equations ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Degree Theory ◽  
Linear Operators ◽  
Singular Boundary ◽  
Singular Boundary Value Problems ◽  
Topological Degree Theory ◽  
Nontrivial Solutions ◽  
Third Order

AbstractThe singular boundary value problems of third-order differential equations $$ \begin{array}{*{20}c} { - u'''(t) = h(t)f(t,u(t)), t \in (0,1),} \\ {u(0) = u'(0) = 0, u'(1) = \alpha u'(\eta )} \\ \end{array} $$ are considered under some conditions concerning the first eigenvalues corresponding to the relevant linear operators, where h(t) is allowed to be singular at both t = 0 and t = 1, and f is not necessary to be nonnegative. The existence results of nontrivial solutions and positive solutions are given by means of the topological degree theory.

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