scholarly journals Existence of Solutions for Fractionalq-Integrodifference Equations with Nonlocal Fractionalq-Integral Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Suphawat Asawasamrit ◽  
Jessada Tariboon ◽  
Sotiris K. Ntouyas
Keyword(s):  
Integral Boundary Conditions ◽  
Integrodifference Equations ◽  
Integral Conditions ◽  
Uniqueness Of Solutions ◽  
Integral Boundary ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Quantum Numbers ◽  
Nonlinear Alternative ◽  
Banach Contraction ◽  
The Banach Contraction Principle

We study a class of fractionalq-integrodifference equations with nonlocal fractionalq-integral boundary conditions which have different quantum numbers. By applying the Banach contraction principle, Krasnoselskii’s fixed point theorem, and Leray-Schauder nonlinear alternative, the existence and uniqueness of solutions are obtained. In addition, some examples to illustrate our results are given.

scholarly journals Existence Theory for a Fractional q-Integro-Difference Equation with q-Integral Boundary Conditions of Different Orders

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 659 ◽  
Author(s):  
Sina Etemad ◽  
Sotiris K. Ntouyas ◽  
Bashir Ahmad
Keyword(s):  
Boundary Conditions ◽  
Integral Boundary Conditions ◽  
Contraction Mapping Principle ◽  
Uniqueness Result ◽  
Existence Theory ◽  
Integral Boundary ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
New Class ◽  
Nonlinear Alternative ◽  
Banach Contraction

In this paper, we study the existence of solutions for a new class of fractional q-integro-difference equations involving Riemann-Liouville q-derivatives and a q-integral of different orders, supplemented with boundary conditions containing q-integrals of different orders. The first existence result is obtained by means of Krasnoselskii’s fixed point theorem, while the second one relies on a Leray-Schauder nonlinear alternative. The uniqueness result is derived via the Banach contraction mapping principle. Finally, illustrative examples are presented to show the validity of the obtained results. The paper concludes with some interesting observations.

scholarly journals Sequential Riemann–Liouville and Hadamard–Caputo Fractional Differential Systems with Nonlocal Coupled Fractional Integral Boundary Conditions

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 174
Author(s):  
Chanakarn Kiataramkul ◽  
Weera Yukunthorn ◽  
Sotiris K. Ntouyas ◽  
Jessada Tariboon
Keyword(s):  
Boundary Conditions ◽  
Fractional Integral ◽  
Integral Boundary Conditions ◽  
Contraction Mapping Principle ◽  
Uniqueness Of Solutions ◽  
Caputo Fractional Derivatives ◽  
Integral Boundary ◽  
Banach Contraction ◽  
Fractional Differential ◽  
Banach Contraction Mapping Principle

In this paper, we initiate the study of existence of solutions for a fractional differential system which contains mixed Riemann–Liouville and Hadamard–Caputo fractional derivatives, complemented with nonlocal coupled fractional integral boundary conditions. We derive necessary conditions for the existence and uniqueness of solutions of the considered system, by using standard fixed point theorems, such as Banach contraction mapping principle and Leray–Schauder alternative. Numerical examples illustrating the obtained results are also presented.

scholarly journals Sequential Derivatives of Nonlinearq-Difference Equations with Three-Pointq-Integral Boundary Conditions

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Nittaya Pongarm ◽  
Suphawat Asawasamrit ◽  
Jessada Tariboon
Keyword(s):  
Boundary Conditions ◽  
Difference Equations ◽  
Contraction Mapping ◽  
Sufficient Conditions ◽  
Degree Theory ◽  
Integral Boundary Conditions ◽  
Integral Boundary ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Quantum Numbers ◽  
Derivatives Of

This paper studies sufficient conditions for the existence of solutions to the problem of sequential derivatives of nonlinearq-difference equations with three-pointq-integral boundary conditions. Our results are concerned with several quantum numbers of derivatives and integrals. By using Banach's contraction mapping, Krasnoselskii's fixed-point theorem, and Leray-Schauder degree theory, some new existence results are obtained. Two examples illustrate our results.

scholarly journals Noninstantaneous Impulsive Fractional Quantum Hahn Integro-Difference Boundary Value Problems

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 671 ◽  
Author(s):  
Surang Sitho ◽  
Chayapat Sudprasert ◽  
Sotiris K. Ntouyas ◽  
Jessada Tariboon
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Integral Boundary Conditions ◽  
Contraction Mapping Principle ◽  
Integral Boundary ◽  
Fractional Quantum ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Nonlinear Alternative ◽  
Banach Contraction

In this paper, we study the existence and uniqueness results for noninstantaneous impulsive fractional quantum Hahn integro-difference boundary value problems with integral boundary conditions, by using Banach contraction mapping principle and Leray–Schauder nonlinear alternative. Examples are included illustrating the obtained results. To the best of our knowledge, no work has reported on the existence of solutions to the Hahn-difference equation with noninstantaneous impulses.

scholarly journals An Analytical Survey on the Solutions of the Generalized Double-Order φ -Integrodifferential Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Sh. Rezapour ◽  
S. K. Ntouyas ◽  
M. Q. Iqbal ◽  
A. Hussain ◽  
S. Etemad ◽  
...  
Keyword(s):  
Fixed Point ◽  
Boundary Conditions ◽  
Integrodifferential Equation ◽  
Existence Of Solutions ◽  
Integral Boundary Conditions ◽  
Banach Contraction Principle ◽  
Integral Boundary ◽  
Banach Contraction ◽  
The Banach Contraction Principle ◽  
Schauder Fixed Point

We study the existence of solutions for a newly configured model of a double-order integrodifferential equation including φ -Caputo double-order φ -integral boundary conditions. In this way, we use the Krasnoselskii and Leray-Schauder fixed point results. Also, we invoke the Banach contraction principle to confirm the uniqueness of the existing solutions. Finally, we provide three examples to illustrate our analytical findings.

Nonlocal Fractional Boundary Value Problems with Slit-Strips Boundary Conditions

2015 ◽  
Vol 18 (1) ◽  
Author(s):  
Bashir Ahmad ◽  
Sotiris K. Ntouyas
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Integral Boundary Conditions ◽  
Contraction Mapping Principle ◽  
Uniqueness Of Solutions ◽  
Integral Boundary ◽  
Nonlinear Alternative ◽  
Differential Equations And Inclusions

AbstractIn this paper, we study nonlocal boundary value problems of fractional differential equations and inclusions with slit-strips integral boundary conditions. We show the existence and uniqueness of solutions for the single valued case (equations) by means of classical contraction mapping principle while the existence result is obtained via a fixed point theorem due to D. O'Regan. The existence of solutions for the multivalued case (inclusions) is established via nonlinear alternative for contractive maps. The results are well illustrated with the aid of examples.

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 Existence Results for a Class of Coupled Hilfer Fractional Pantograph Differential Equations with Nonlocal Integral Boundary Value Conditions

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Karim Guida ◽  
Khalid Hilal ◽  
Lahcen Ibnelazyz
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Integral Boundary Conditions ◽  
Coupled Systems ◽  
Uniqueness Of Solutions ◽  
Integral Boundary ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
New Class ◽  
Nonlocal Integral Boundary Conditions ◽  
Banach’S Contraction Principle

This paper deals with the existence and uniqueness of solutions for a new class of coupled systems of Hilfer fractional pantograph differential equations with nonlocal integral boundary conditions. First of all, we are going to give some definitions that are necessary for the understanding of the manuscript; second of all, we are going to prove our main results using the fixed point theorems, namely, Banach’s contraction principle and Krasnoselskii’s fixed point theorem; in the end, we are giving two examples to illustrate our results.

scholarly journals Existence results for nonlinear fractional q-difference equations with nonlocal Riemann-Liouville q-integral boundary conditions

Filomat ◽  
2016 ◽  
Vol 30 (9) ◽  
pp. 2521-2533 ◽  
Author(s):  
Wengui Yang
Keyword(s):  
Fixed Point ◽  
Boundary Conditions ◽  
Difference Equations ◽  
Fixed Point Theory ◽  
Integral Boundary Conditions ◽  
Point Theory ◽  
Uniqueness Of Solutions ◽  
Integral Boundary ◽  
Nonlinear Alternative ◽  
Krasnoselskii Fixed Point Theorem

This paper deals with the existence and uniqueness of solutions for a class of nonlinear fractional q-difference equations boundary value problems involving four-point nonlocal Riemann-Liouville q-integral boundary conditions of different order. Our results are based on some well-known tools of fixed point theory such as Banach contraction principle, Krasnoselskii fixed point theorem, and the Leray-Schauder nonlinear alternative. As applications, some interesting examples are presented to illustrate the main results.

scholarly journals Existence and Uniqueness of Solutions for the Nonlinear Fractional Differential Equations with Two-point and Integral Boundary Conditions

2021 ◽  
Vol 14 (2) ◽  
pp. 608-617
Author(s):  
Yagub Sharifov ◽  
S.A. Zamanova ◽  
R.A. Sardarova
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Integral Boundary Conditions ◽  
Contraction Mapping Principle ◽  
Uniqueness Of Solutions ◽  
Integral Boundary ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Fractional Differential

In this paper the existence and uniqueness of solutions to the fractional differential equations with two-point and integral boundary conditions is investigated. The Green function is constructed, and the problem under consideration is reduced to the equivalent integral equation. Existence and uniqueness of a solution to this problem is analyzed using the Banach the contraction mapping principle and Krasnoselskii’s fixed point theorem.

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