scholarly journals Application of fixed point theorem for stability analysis of a nonlinear Schrodinger with Caputo-Liouville derivative

Filomat ◽  
2017 ◽  
Vol 31 (8) ◽  
pp. 2243-2248 ◽  
Author(s):  
Abdon Atangana ◽  
Dumitru Baleanu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fractional Order ◽  
Point Theorem ◽  
Iteration Scheme ◽  
Iterative Approach ◽  
Liouville Derivative ◽  
The Fixed Point Theorem ◽  
The Stability ◽  
Modified Equation

Using the new Caputo-Liouville derivative with fractional order, we have modified the nonlinear Schrdinger equation. We have shown some useful in connection of the new derivative with fractional order. We used an iterative approach to derive an approximate solution of the modified equation. We have established the stability of the iteration scheme using the fixed point theorem. We have in addition presented in detail the uniqueness of the special solution.

Nonlocal Riemann–Liouville fractional evolution inclusions in Banach space

2020 ◽  
Vol 13 (08) ◽  
pp. 2050162
Author(s):  
Shamas Bilal ◽  
Tzanko Donchev ◽  
Nikolay Kitanov ◽  
Nasir Javaid
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Evolution Inclusions ◽  
Liouville Derivative ◽  
The Fixed Point Theorem ◽  
General Banach Space

In this paper, we study the existence of solutions for nonlocal semilinear fractional evolution inclusions involving Riemann–Liouville derivative in a general Banach space. The fixed point theorem for contractive valued multifunction is used. Illustrative example is provided.

scholarly journals The Stability of a General Sextic Functional Equation by Fixed Point Theory

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Jaiok Roh ◽  
Yang-Hi Lee ◽  
Soon-Mo Jung
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theory ◽  
Point Theory ◽  
The Fixed Point Theorem ◽  
The Stability

In this paper, we will consider the generalized sextic functional equation ∑ i = 0 7   7 C i − 1 7 − i f x + i y = 0 . And by applying the fixed point theorem in the sense of C a ˘ dariu and Radu, we will discuss the stability of the solutions for this functional equation.

scholarly journals Existence of Positive Periodic Solutions for a Class ofn-Species Competition Systems with Impulses

2011 ◽  
Vol 2011 ◽  
pp. 1-9
Author(s):  
Peilian Guo ◽  
Yansheng Liu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Sufficient Conditions ◽  
Species Competition ◽  
Positive Periodic Solutions ◽  
The Fixed Point Theorem

By using the fixed point theorem on cone, some sufficient conditions are obtained on the existence of positive periodic solutions for a class ofn-species competition systems with impulses. Meanwhile, we point out that the conclusion of (Yan, 2009) is incorrect.

Existence, uniqueness and limit property of solutions to quadratic Erdélyi-Kober type integral equations of fractional order

Open Physics ◽  
2013 ◽  
Vol 11 (6) ◽  
Author(s):  
JinRong Wang ◽  
Chun Zhu ◽  
Michal Fečkan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Fractional Order ◽  
Point Theorem ◽  
Measure Of Noncompactness ◽  
Existence Results ◽  
Limit Property ◽  
Type Integral

AbstractIn this paper, we apply certain measure of noncompactness and fixed point theorem of Darbo type to derive the existence and limit property of solutions to quadratic Erdélyi-Kober type integral equations of fractional order with three parameters. Moreover, we also present the uniqueness and another existence results of the solutions to the above equations. Finally, two examples are given to illustrate the obtained results.

Self‐defeating predictions and the fixed‐point theorem: A refutation

Inquiry ◽  
1982 ◽  
Vol 25 (3) ◽  
pp. 331-352 ◽  
Author(s):  
Audun Øfsti ◽  
Dag Østerberg
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
The Fixed Point Theorem

scholarly journals The Impulsive Neutral Integro-Differential Equations with Infinite Delay and Non-Instantaneous Impulses

2018 ◽  
Vol 7 (4.10) ◽  
pp. 694
Author(s):  
V. Usha ◽  
M. Mallika Arjunan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Banach Spaces ◽  
Point Theorem ◽  
Infinite Delay ◽  
Semigroup Theory ◽  
Existence Results ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
The Fixed Point Theorem

In this manuscript, we work to accomplish the Krasnoselskii's fixed point theorem to analyze the existence results for an impulsive neutral integro-differential equations  with infinite delay and non-instantaneous impulses in Banach spaces. By deploying the fixed point theorem with semigroup theory, we developed the coveted outcomes.   

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 A fixed point theorem in H-space and related results

1990 ◽  
Vol 42 (1) ◽  
pp. 133-140 ◽  
Author(s):  
E. Tarafdar
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Minimax Inequalities ◽  
The Fixed Point Theorem

The equivalence of a fixed point theorem and the Fan-Knaster-Kuratowski-Mazurkiewicz theorem in H-space has been established. The fixed point theorem is then applied to obtain a theorem on sets with H-convex sections, and also results on minimax inequalities.

Sign in / Sign up

Export Citation Format

Share Document