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 A new class of mixed fractional differential equations with integral boundary conditions

2021 ◽  
Vol 7 (2) ◽  
pp. 227-247
Author(s):  
Djiab Somia ◽  
Nouiri Brahim
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Integral Boundary Conditions ◽  
Contraction Mapping Principle ◽  
Integral Boundary ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
New Class ◽  
Fractional Differential ◽  
Equivalence Result

AbstractThis paper deals with a new class of mixed fractional differential equations with integral boundary conditions. We show an important equivalence result between our problem and nonlinear integral Fredholm equation of the second kind. The existence and uniqueness of a positive solution are proved using Guo-Krasnoselskii’s fixed point theorem and Banach’s contraction mapping principle. Different types of Ulam-Hyers stability are discussed. Three examples are also given to show the applicability of our results.

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 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 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.

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.

Analysis of fractional integro-differential equations with nonlocal Erdélyi-Kober type integral boundary conditions

2020 ◽  
Vol 23 (5) ◽  
pp. 1401-1415
Author(s):  
Palanisamy Duraisamy ◽  
Thangaraj Nandha Gopal ◽  
Muthaiah Subramanian
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Contraction Mapping ◽  
Fixed Point Theorems ◽  
Integral Boundary Conditions ◽  
Contraction Mapping Principle ◽  
Uniqueness Result ◽  
Uniqueness Of Solutions ◽  
Integral Boundary ◽  
Type Integral

Abstract In this article, we study the existence and uniqueness of solutions for nonlinear fractional integro-differential equations with nonlocal Erdélyi-Kober type integral boundary conditions. The existence results are based on Krasnoselskii’s and Schaefer’s fixed point theorems, whereas the uniqueness result is based on the contraction mapping principle. Examples illustrating the applicability of our main results are also constructed.

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.

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 Non-Linear First-Order Differential Boundary Problems with Multipoint and Integral Conditions

2021 ◽  
Vol 5 (1) ◽  
pp. 15
Author(s):  
Misir J. Mardanov ◽  
Yagub A. Sharifov ◽  
Yusif S. Gasimov ◽  
Carlo Cattani
Keyword(s):  
Integral Equation ◽  
Integral Boundary Conditions ◽  
Contraction Mapping Principle ◽  
Boundary Problems ◽  
Integral Boundary ◽  
Multipoint Problem ◽  
First Order ◽  
Banach Contraction ◽  
First Time ◽  
Banach Contraction Mapping Principle

This paper considers boundary value problem (BVP) for nonlinear first-order differential problems with multipoint and integral boundary conditions. A suitable Green function was constructed for the first time in order to reduce this problem into a corresponding integral equation. So that by using the Banach contraction mapping principle (BCMP) and Schaefer’s fixed point theorem (SFPT) on the integral equation, we can show that the solution of the multipoint problem exists and it is unique.

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