scholarly journals Separate Fractional (p,q)-Integrodifference Equations via Nonlocal Fractional (p,q)-Integral Boundary Conditions

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2212
Author(s):  
Thongchai Dumrongpokaphan ◽  
Sotiris K. Ntouyas ◽  
Thanin Sitthiwirattham
Keyword(s):  
Fixed Point ◽  
Boundary Conditions ◽  
Integral Boundary Conditions ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Integrodifference Equations ◽  
Integral Boundary ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Point Operator

In this paper, we study a boundary value problem involving (p,q)-integrodifference equations, supplemented with nonlocal fractional (p,q)-integral boundary conditions with respect to asymmetric operators. First, we convert the given nonlinear problem into a fixed-point problem, by considering a linear variant of the problem at hand. Once the fixed-point operator is available, existence and uniqueness results are established using the classical Banach’s and Schaefer’s fixed-point theorems. The application of the main results is demonstrated by presenting numerical examples. Moreover, we study some properties of (p,q)-integral that are used in our study.

scholarly journals On a boundary value problem for fractional Hahn integro-difference equations with four-point fractional integral boundary conditions

2021 ◽  
Vol 7 (1) ◽  
pp. 632-650
Author(s):  
Varaporn Wattanakejorn ◽  
◽  
Sotiris K. Ntouyas ◽  
Thanin Sitthiwirattham ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Boundary Value ◽  
Integral Boundary Conditions ◽  
Difference Operators ◽  
Point Problem ◽  
Integral Boundary ◽  
Uniqueness Results ◽  
Fractional Hahn Integral

<abstract><p>In this paper, we study a boundary value problem consisting of Hahn integro-difference equation supplemented with four-point fractional Hahn integral boundary conditions. The novelty of this problem lies in the fact that it contains two fractional Hahn difference operators and three fractional Hahn integrals with different quantum numbers and orders. Firstly, we convert the given nonlinear problem into a fixed point problem, by considering a linear variant of the problem at hand. Once the fixed point operator is available, we make use the classical Banach's and Schauder's fixed point theorems to establish existence and uniqueness results. An example is also constructed to illustrate the main results. Several properties of fractional Hahn integral that will be used in our study are also discussed.</p></abstract>

scholarly journals Existence and Uniqueness of the Solution for an Integral Equation with Supremum, via w-Distances

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1554 ◽  
Author(s):  
Veronica Ilea ◽  
Diana Otrocol
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Existence And Uniqueness ◽  
Stability Result ◽  
Fixed Point Problem ◽  
Comparison Theorems ◽  
Point Problem ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Uniqueness Of The Solution

Following the idea of T. Wongyat and W. Sintunavarat, we obtain some existence and uniqueness results for the solution of an integral equation with supremum. The paper ends with the study of Gronwall-type theorems, comparison theorems and a result regarding a Ulam–Hyers stability result for the corresponding fixed point problem.

scholarly journals A STUDY OF NONLINEAR FRACTIONAL-ORDER BOUNDARY VALUE PROBLEM WITH NONLOCAL ERDELYI-KOBER AND GENERALIZED RIEMANN-LIOUVILLE TYPE INTEGRAL BOUNDARY CONDITIONS

2017 ◽  
Vol 22 (2) ◽  
pp. 121-139 ◽  
Author(s):  
Bashir Ahmad ◽  
Sotiris K. Ntouyas ◽  
Jessada Tariboon ◽  
Ahmed Alsaedi
Keyword(s):  
Boundary Conditions ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Integral Boundary Conditions ◽  
Fractional Integrals ◽  
Integral Boundary ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Caputo Fractional Differential Equations ◽  
The Given

We investigate a new kind of nonlocal boundary value problems of nonlinear Caputo fractional differential equations supplemented with integral boundary conditions involving Erdelyi-Kober and generalized Riemann-Liouville fractional integrals. Existence and uniqueness results for the given problem are obtained by means of standard fixed point theorems. Examples illustrating the main results are also discussed.

scholarly journals On the Generalization of a Solution for a Class of Integro-Differential Equations with Nonseparated Integral Boundary Conditions

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Yanyuan Xing ◽  
Feng Jiao ◽  
Fang Liu
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Existence And Uniqueness ◽  
Degree Theory ◽  
Integral Boundary Conditions ◽  
Integral Boundary ◽  
Existence And Uniqueness Results ◽  
Main Work ◽  
Uniqueness Results ◽  
Type Integral

In this paper, the existence and uniqueness results of the generalization nonlinear fractional integro-differential equations with nonseparated type integral boundary conditions are investigated. A natural formula of solutions is derived and some new existence and uniqueness results are obtained under some conditions for this class of problems by using standard fixed point theorems and Leray–Schauder degree theory, which extend and supplement some known results. Some examples are discussed for the illustration of the main work.

scholarly journals ON EXISTENCE OF SOLUTIONS FOR NONLINEAR Q-DIFFERENCE EQUATIONS WITH NONLOCAL Q-INTEGRAL BOUNDARY CONDITIONS

2015 ◽  
Vol 20 (5) ◽  
pp. 604-618 ◽  
Author(s):  
Ravi P. Agarwal ◽  
Guotao Wang ◽  
Bashir Ahmad ◽  
Lihong Zhang ◽  
Aatef Hobiny ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Existence Of Solutions ◽  
Fixed Point Theory ◽  
Sufficient Conditions ◽  
Integral Boundary Conditions ◽  
Point Theory ◽  
Integral Boundary ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
The Given

In this paper, we discuss the existence of solutions for nonlinear qdifference equations with nonlocal q-integral boundary conditions. The first part of the paper deals with some existence and uniqueness results obtained by means of standard tools of fixed point theory. In the second part, sufficient conditions for the existence of extremal solutions for the given problem are established. The results are well illustrated with the aid of examples.

scholarly journals On Coupled Systems for Hilfer Fractional Differential Equations with Nonlocal Integral Boundary Conditions

2020 ◽  
Vol 2020 ◽  
pp. 1-12 ◽  
Author(s):  
Athasit Wongcharoen ◽  
Sotiris K. Ntouyas ◽  
Jessada Tariboon
Keyword(s):  
Boundary Conditions ◽  
Integral Boundary Conditions ◽  
Coupled System ◽  
Contraction Mapping Principle ◽  
Coupled Systems ◽  
Integral Boundary ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Nonlocal Integral Boundary Conditions

In this paper, we study a coupled system involving Hilfer fractional derivatives with nonlocal integral boundary conditions. Existence and uniqueness results are obtained by applying Leray-Schauder alternative, Krasnoselskii’s fixed point theorem, and Banach’s contraction mapping principle. Examples illustrating our results are also presented.

scholarly journals Fractional Langevin Equations with Nonlocal Integral Boundary Conditions

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 402 ◽  
Author(s):  
Ahmed Salem ◽  
Faris Alzahrani ◽  
Lamya Almaghamsi
Keyword(s):  
Boundary Conditions ◽  
Integral Boundary Conditions ◽  
Langevin Equations ◽  
Integral Boundary ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Nonlinear Alternative ◽  
Banach Contraction ◽  
Nonlocal Integral Boundary Conditions ◽  
Fractional Orders

In this paper, we investigate a class of nonlinear Langevin equations involving two fractional orders with nonlocal integral and three-point boundary conditions. Using the Banach contraction principle, Krasnoselskii’s and the nonlinear alternative Leray Schauder theorems, the existence and uniqueness results of solutions are proven. The paper was appended examples which illustrate the applicability of the results.

scholarly journals A fixed point approach to the solution of singular fractional differential equations with integral boundary conditions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Kalaivani Chandran ◽  
Kalpana Gopalan ◽  
Sumaiya Tasneem Zubair ◽  
Thabet Abdeljawad
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Integral Boundary Conditions ◽  
Fixed Point Problem ◽  
Point Problem ◽  
List Type ◽  
Uniqueness Of Solutions ◽  
Integral Boundary ◽  
Fractional Differential

AbstractIn this article, we first demonstrate a fixed point result under certain contraction in the setting of controlled b-Branciari metric type spaces. Thereafter, we specifically consider a following boundary value problem (BVP) for a singular fractional differential equation of order α: $$ \begin{aligned} &{}^{c}D^{\alpha }v(t) + h \bigl(t,v(t) \bigr) = 0,\quad 0< t< 1, \\ &v''(0) = v'''(0) = 0, \\ &v'(0) = v(1) = \beta \int _{0}^{1} v(s) \,ds, \end{aligned} $$ D α c v ( t ) + h ( t , v ( t ) ) = 0 , 0 < t < 1 , v ″ ( 0 ) = v ‴ ( 0 ) = 0 , v ′ ( 0 ) = v ( 1 ) = β ∫ 0 1 v ( s ) d s , where $3<\alpha <4$ 3 < α < 4 , $0<\beta <2$ 0 < β < 2 , ${}^{c}D^{\alpha }$ D α c is the Caputo fractional derivative and h may be singular at $v = 0$ v = 0 . Eventually, we investigate the existence and uniqueness of solutions of the aforementioned boundary value problem of order α via a fixed point problem of an integral operator.

scholarly journals Boundary value problems for Caputo fractional differential equations with nonlocal and fractional integral boundary conditions

2020 ◽  
Vol 9 (3) ◽  
pp. 531-544
Author(s):  
Choukri Derbazi ◽  
Hadda Hammouche
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Fractional Integral ◽  
Integral Boundary Conditions ◽  
Integral Boundary ◽  
Uniqueness Results ◽  
Fractional Differential

Abstract In this paper, we study the existence and uniqueness of solutions for fractional differential equations with nonlocal and fractional integral boundary conditions. New existence and uniqueness results are established using the Banach contraction principle. Other existence results are obtained using O’Regan fixed point theorem and Burton and Kirk fixed point. In addition, an example is given to demonstrate the application of our main results.

scholarly journals Analysis of implicit type of a generalized fractional differential equations with nonlinear integral boundary conditions

2020 ◽  
Vol 1 (1) ◽  
pp. 64-76
Author(s):  
Saleh Redhwan ◽  
Sadikali Shaikh
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Integral Boundary Conditions ◽  
Integral Boundary ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Fractional Differential ◽  
The Given

The given paper describes the implicit fractional differential equation with nonlinear integral boundary conditions in the frame of Caputo-Katugampola fractional derivative. We obtain an analogous integral equation of the given problem and prove the existence and uniqueness results of such a problem using the Banach and Krasnoselskii fixed point theorems. To show the effectiveness of the acquired results, convenient examples are presented.

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