Existence and Ulam Stability Criteria for Antiperiodic Boundary Value Problem of Fractional Difference Equation

2021 ◽  
pp. 173-184
Author(s):  
A. George Maria Selvam ◽  
R. Dhineshbabu
Keyword(s):  
Difference Equation ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Ulam Stability ◽  
Stability Criteria ◽  
Fractional Difference ◽  
Fractional Difference Equation

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.

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.

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 On a nonlinear sequential four-point fractional q-difference equation involving q-integral operators in boundary conditions along with stability criteria

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Abdelatif Boutiara ◽  
Sina Etemad ◽  
Jehad Alzabut ◽  
Azhar Hussain ◽  
Muthaiah Subramanian ◽  
...  
Keyword(s):  
Difference Equation ◽  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Integral Operators ◽  
Stability Criteria ◽  
Uniqueness Of Solutions ◽  
Fractional Quantum ◽  
Condensing Operators

AbstractIn this paper, we consider a nonlinear sequential q-difference equation based on the Caputo fractional quantum derivatives with nonlocal boundary value conditions containing Riemann–Liouville fractional quantum integrals in four points. In this direction, we derive some criteria and conditions of the existence and uniqueness of solutions to a given Caputo fractional q-difference boundary value problem. Some pure techniques based on condensing operators and Sadovskii’s measure and the eigenvalue of an operator are employed to prove the main results. Also, the Ulam–Hyers stability and generalized Ulam–Hyers stability are investigated. We examine our results by providing two illustrative examples.

scholarly journals Existence and Ulam Stability of Solutions for Discrete Fractional Boundary Value Problem

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Fulai Chen ◽  
Yong Zhou
Keyword(s):  
Boundary Value Problem ◽  
Difference Equations ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Ulam Stability ◽  
Stability Of Solutions ◽  
Fractional Boundary Value Problem ◽  
Fractional Difference ◽  
Fractional Difference Equations

We discuss the existence of solutions for antiperiodic boundary value problem and the Ulam stability for nonlinear fractional difference equations. Two examples are also provided to illustrate our main results.

scholarly journals Hyers - Ulam Stability Results for Discrete Antiperiodic Boundary Value Problem with Fractional Order 2 <  3

2019 ◽  
Vol 9 (1) ◽  
pp. 4997-5003 ◽  
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Fractional Order ◽  
Difference Operator ◽  
Boundary Value ◽  
Ulam Stability ◽  
Fractional Difference ◽  
Stability Results

In this present work, we investigate Ulam stability for the following nonlinear discrete antiperiodic boundary value problem with fractional order of the form 0 ( ) = 1, ( 1) ,   C k v k k v k          for   0 k L L    [0, 2] = 0,1,..., 2  , with boundary conditions v v L ( 3) = ( )      ,     v v L ( 3) = ( )   , 2 2     v v L ( 3) = ( )   , where 2 :[ 2, ] L             is a continuous and 0 C k   is the Caputo fractional difference operator with order 2 < 3   . Finally, the main results are illustrated by some examples.

scholarly journals Existence and Uniqueness of Solutions for a Discrete Fractional Mixed Type Sum-Difference Equation Boundary Value Problem

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Weidong Lv
Keyword(s):  
Difference Equation ◽  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Mixed Type ◽  
Contraction Mapping ◽  
Boundary Value ◽  
Contraction Mapping Principle ◽  
Uniqueness Of Solutions ◽  
Fractional Difference ◽  
Equation Boundary

By means of Schauder’s fixed point theorem and contraction mapping principle, we establish the existence and uniqueness of solutions to a boundary value problem for a discrete fractional mixed type sum-difference equation with the nonlinear term dependent on a fractional difference of lower order. Moreover, a suitable choice of a Banach space allows the solutions to be unbounded and two representative examples are presented to illustrate the effectiveness of the main results.

scholarly journals Ulam stability results for boundary value problem of fractional difference equations

2020 ◽  
pp. 219-230
Author(s):  
A. George Maria Selvam ◽  
R. Dhineshbabu
Keyword(s):  
Stability Analysis ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Fractional Order ◽  
Difference Equations ◽  
Difference Operator ◽  
Boundary Value ◽  
Ulam Stability ◽  
Fractional Difference ◽  
Stability Results

Boundary value problems have wide applications in science and technology. This paper is concerned with various kinds of Ulam stability analysis for the nonlinear discrete boundary value problem of fractional order $\sigma\in(2,3]$ with Riemann-Liouville fractional difference operator. Finally, some examples are presented to illustrate the 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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