Fixed point theorem for measurable field of operators with an application to random differential equation

1988 ◽  
pp. 581-587 ◽  
Author(s):  
T. A. Ždanok
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Random Differential Equation ◽  
Measurable Field

scholarly journals Multiplicity Result of Positive Solutions for Nonlinear Differential Equation of Fractional Order

2012 ◽  
Vol 2012 ◽  
pp. 1-15
Author(s):  
Yang Liu ◽  
Zhang Weiguo
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Nonlinear Differential Equation ◽  
Positive Solutions ◽  
Fractional Order ◽  
Point Theorem ◽  
Boundary Value ◽  
Order Derivative ◽  
Fractional Order Derivative

We investigate the existence of multiple positive solutions for a class of boundary value problems of nonlinear differential equation with Caputo’s fractional order derivative. The existence results are obtained by means of the Avery-Peterson fixed point theorem. It should be point out that this is the first time that this fixed point theorem is used to deal with the boundary value problem of differential equations with fractional order derivative.

scholarly journals Fixed Point Theorems Applied in Uncertain Fractional Differential Equation with Jump

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 765
Author(s):  
Zhifu Jia ◽  
Xinsheng Liu ◽  
Cunlin Li
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fractional Differential Equation ◽  
Growth Condition ◽  
Lipschitz Condition ◽  
Point Theorem ◽  
Linear Growth ◽  
Linear Growth Condition ◽  
Fractional Differential

No previous study has involved uncertain fractional differential equation (FDE, for short) with jump. In this paper, we propose the uncertain FDEs with jump, which is driven by both an uncertain V-jump process and an uncertain canonical process. First of all, for the one-dimensional case, we give two types of uncertain FDEs with jump that are symmetric in terms of form. The next, for the multidimensional case, when the coefficients of the equations satisfy Lipschitz condition and linear growth condition, we establish an existence and uniqueness theorems of uncertain FDEs with jump of Riemann-Liouville type by Banach fixed point theorem. A symmetric proof in terms of form is suitable to the Caputo type. When the coefficients do not satisfy the Lipschitz condition and linear growth condition, we just prove an existence theorem of the Caputo type equation by Schauder fixed point theorem. In the end, we present an application about uncertain interest rate model.

scholarly journals Controllability Analysis for Impulsive Integro-differential Equation via AB Fractional Derivative

2021 ◽  
Author(s):  
KALIMUTHU KALIRAJ ◽  
E. Thilakraj ◽  
Ravichandran C ◽  
Kottakkaran Nisar
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Fractional Derivative ◽  
Fractional Order ◽  
Point Theorem ◽  
Nonlocal Conditions ◽  
Banach Fixed Point Theorem ◽  
Integro Differential Equation

In this work, we analyse the controllability for certain classes of impulsive integro - differential equations(IIDE) of fractional order via Atangana Baleanu derivative involving finite delay with initial and nonlocal conditions using Banach fixed point theorem.

scholarly journals Existence and Uniqueness for the Controllability of a Dynamical System

2019 ◽  
pp. 168-173
Author(s):  
Eli Innocent Cleopas ◽  
Godspower C. Abanum
Keyword(s):  
Dynamical System ◽  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Integro Differential Equation ◽  
Darbo’S Fixed Point Theorem

In this paper, we consider the existence and uniqueness for the controllability of a dynamical system. Here, measure of non-compactness of set was employed to examine the conditions for darbo’s fixed point theorem which is used to established the existence and uniqueness solution for nonlinear integro-differential equation with implicit derivatives.

scholarly journals Applications of Krasnoselskii-Dhage Type Fixed-Point Theorems to Fractional Hybrid Differential Equations

2021 ◽  
Vol 52 ◽  
Author(s):  
Habibulla Akhadkulov ◽  
Fahad Alsharari ◽  
Teh Yuan Ying
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Integral Operators ◽  
Existence Of A Solution ◽  
Hybrid Differential Equation ◽  
Hybrid Differential Equations

In this paper, we prove the existence of a solution of a fractional hybrid differential equation involving the Riemann-Liouville differential and integral operators by utilizing a new version of Kransoselskii-Dhage type fixed-point theorem obtained in [13]. Moreover, we provide an example to support our result.

scholarly journals Three Positive Solutions for Boundary Value Problem of Fractional q-Differential Equation

2019 ◽  
Vol 12 (1) ◽  
pp. 12
Author(s):  
Yaoyao Luo
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Difference Equation ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Point Theorem ◽  
Boundary Value

In this paper, we study the boundary value problem of a Riemann-Liouville fractional q-difference equation. By applying the Leggett-Williams fixed point theorem and the properties of the Green’s function, three positive solutions are obtained.

Sign in / Sign up

Export Citation Format

Share Document