scholarly journals Stability analysis by fixed point theorems for a class of non-linear Caputo nabla fractional difference equation

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Rabia Ilyas Butt ◽  
Thabet Abdeljawad ◽  
Mujeeb ur Rehman
Keyword(s):  
Fixed Point ◽  
Stability Analysis ◽  
Difference Equation ◽  
Fixed Point Theorems ◽  
Fractional Difference ◽  
Fractional Difference Equation ◽  
Non Linear

scholarly journals On Nonlinear Fractional Difference Equation with Delay and Impulses

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 980 ◽  
Author(s):  
Rujira Ouncharoen ◽  
Saowaluck Chasreechai ◽  
Thanin Sitthiwirattham
Keyword(s):  
Fixed Point ◽  
Difference Equation ◽  
Fixed Point Theorems ◽  
Existence Results ◽  
Fractional Difference ◽  
Fractional Difference Equation ◽  
Equation With Delay

In this paper, we establish the existence results for a nonlinear fractional difference equation with delay and impulses. The Banach and Schauder’s fixed point theorems are employed as tools to study the existence of its solutions. We obtain the theorems showing the conditions for existence results. Finally, we provide an example to show the applicability of our results.

scholarly journals Positive Solutions for Boundary Value Problem of Nonlinear Fractional -Difference Equation

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
Moustafa El-Shahed ◽  
Farah M. Al-Askar
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Difference Equation ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Boundary Value ◽  
Multiple Positive Solutions ◽  
Fractional Boundary Value Problem ◽  
Fractional Difference ◽  
Fractional Difference Equation

We investigate the existence of multiple positive solutions to the nonlinear -fractional boundary value problem , , by using a fixed point theorem in a cone.

Stability Analysis of p-Laplacian Fractional Difference Equation

2021 ◽  
Vol 30 (1) ◽  
Author(s):  
Rabia Ilyas Butt ◽  
Mujeeb Ur Rehman ◽  
Thabet Abdeljawad ◽  
Gulsen Kilinc
Keyword(s):  
Stability Analysis ◽  
Difference Equation ◽  
Fractional Difference ◽  
Fractional Difference Equation

scholarly journals On the Existence of Three Positive Solutions for a Caputo Fractional Difference Equation

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Lili Kong ◽  
Huiqin Chen ◽  
Luping Li ◽  
Shugui Kang
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Difference Equation ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Point Theorem ◽  
Boundary Value ◽  
Fractional Difference ◽  
Equation Boundary ◽  
Fractional Difference Equation

In this paper, we introduce the application of three fixed point theorem by discussing the existence of three positive solutions for a class of Caputo fractional difference equation boundary value problem. We establish the condition of the existence of three positive solutions for this problem.

Stability analysis of impulsive fractional difference equations

2018 ◽  
Vol 21 (2) ◽  
pp. 354-375 ◽  
Author(s):  
Guo–Cheng Wu ◽  
Dumitru Baleanu
Keyword(s):  
Stability Analysis ◽  
Asymptotic Stability ◽  
Difference Equation ◽  
Fractional Calculus ◽  
Difference Equations ◽  
Discrete Fractional Calculus ◽  
Fractional Difference ◽  
Numerical Result ◽  
Fractional Difference Equations ◽  
Fractional Difference Equation

AbstractWe revisit motivation of the fractional difference equations and some recent applications to image encryption. Then stability of impulsive fractional difference equations is investigated in this paper. The fractional sum equation is considered and impulsive effects are introduced into discrete fractional calculus. A class of impulsive fractional difference equations are proposed. A discrete comparison principle is given and asymptotic stability of nonlinear fractional difference equation are discussed. Finally, an impulsive Mittag–Leffler stability is defined. The numerical result is provided to support the analysis.

scholarly journals On the Oscillation of Non-Linear Fractional Difference Equations with Damping

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 687 ◽  
Author(s):  
Jehad Alzabut ◽  
Velu Muthulakshmi ◽  
Abdullah Özbekler ◽  
Hakan Adıgüzel
Keyword(s):  
Difference Equation ◽  
Riccati Transformation ◽  
Discrete Fractional Calculus ◽  
Damping Term ◽  
Fractional Difference ◽  
Transformation Technique ◽  
Numerical Examples ◽  
Comparison Results ◽  
Fractional Difference Equation ◽  
Non Linear

In studying the Riccati transformation technique, some mathematical inequalities and comparison results, we establish new oscillation criteria for a non-linear fractional difference equation with damping term. Preliminary details including notations, definitions and essential lemmas on discrete fractional calculus are furnished before proceeding to the main results. The consistency of the proposed results is demonstrated by presenting some numerical examples. We end the paper with a concluding remark.

Construction of fixed point operators for nonlinear difference equations of non integer order with impulses

2020 ◽  
Vol 23 (3) ◽  
pp. 886-907
Author(s):  
Syed Sabyel Haider ◽  
Mujeeb Ur Rehman
Keyword(s):  
Fixed Point ◽  
Difference Equation ◽  
Boundary Conditions ◽  
Difference Equations ◽  
Existence Of Solutions ◽  
Nonlinear Difference Equations ◽  
Fractional Difference ◽  
Integer Order ◽  
Fractional Difference Equation ◽  
Point Operator

AbstractIn this article, we establish a technique for transforming arbitrary real order delta difference equations with impulses to corresponding summation equations. The technique is applied to non-integer order delta difference equation with some boundary conditions. Furthermore, the summation formulation for impulsive fractional difference equation is utilized to construct fixed point operator which in turn are used to discuss existence of solutions.

scholarly journals Existence of Solutions for Boundary Value Problem of a Caputo Fractional Difference Equation

2015 ◽  
Vol 2015 ◽  
pp. 1-5
Author(s):  
Zhiping Liu ◽  
Shugui Kang ◽  
Huiqin Chen ◽  
Jianmin Guo ◽  
Yaqiong Cui ◽  
...  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Difference Equation ◽  
Boundary Value Problem ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Discrete Fractional Calculus ◽  
Fractional Difference ◽  
Equation Boundary ◽  
Fractional Difference Equation

We investigate the existence of solutions for a Caputo fractional difference equation boundary value problem. We use Schauder fixed point theorem to deduce the existence of solutions. The proofs are based upon the theory of discrete fractional calculus. We also provide some examples to illustrate our main results.

scholarly journals Non-Trivial Solutions of Non-Autonomous Nabla Fractional Difference Boundary Value Problems

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1101
Author(s):  
Alberto Cabada ◽  
Nikolay D. Dimitrov ◽  
Jagan Mohan Jonnalagadda
Keyword(s):  
Difference Equation ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Existence Results ◽  
Fractional Difference ◽  
Nonlinear Part ◽  
Fractional Difference Equation ◽  
Separated Boundary Conditions ◽  
Series Of Functions ◽  
Schauder Fixed Point

In this article, we present a two-point boundary value problem with separated boundary conditions for a finite nabla fractional difference equation. First, we construct an associated Green’s function as a series of functions with the help of spectral theory, and obtain some of its properties. Under suitable conditions on the nonlinear part of the nabla fractional difference equation, we deduce two existence results of the considered nonlinear problem by means of two Leray–Schauder fixed point theorems. We provide a couple of examples to illustrate the applicability of the established results.

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