EXISTENCE RESULTS FOR A COUPLED SYSTEM OF NONLINEAR FRACTIONAL q-INTEGRO-DIFFERENCE EQUATIONS WITH q-INTEGRAL-COUPLED BOUNDARY CONDITIONS

In this paper, we introduce and investigate a new class of coupled fractional [Formula: see text]-integro-difference equations involving Riemann–Liouville fractional [Formula: see text]-derivatives and [Formula: see text]-integrals of different orders, equipped with [Formula: see text]-integral-coupled boundary conditions. The given problem is converted into an equivalent fixed-point problem by introducing an operator whose fixed-points coincide with solutions of the problem at hand. The existence and uniqueness results for the given problem are, respectively, derived by applying Leray–Schauder nonlinear alternative and Banach contraction mapping principle. Illustrative examples for the obtained results are constructed. This paper concludes with some interesting observations and special cases dealing with uncoupled boundary conditions, and non-integral and integral types nonlinearities.

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Existence and uniqueness results for a nonlinear coupled system involving Caputo fractional derivatives with a new kind of coupled boundary conditions

Applied Mathematics Letters ◽

10.1016/j.aml.2021.107018 ◽

2021 ◽

pp. 107018

Author(s):

Bashir Ahmad ◽

Madeaha Alghanmi ◽

Ahmed Alsaedi ◽

Juan J. Nieto

Keyword(s):

Boundary Conditions ◽

Existence And Uniqueness ◽

Fractional Derivatives ◽

Coupled System ◽

Caputo Fractional Derivatives ◽

Existence And Uniqueness Results ◽

Uniqueness Results ◽

Nonlinear Coupled System ◽

Coupled Boundary Conditions

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A study of a nonlinear coupled system of three fractional differential equations with nonlocal coupled boundary conditions

Advances in Difference Equations ◽

10.1186/s13662-021-03440-7 ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Bashir Ahmad ◽

Soha Hamdan ◽

Ahmed Alsaedi ◽

Sotiris K. Ntouyas

Keyword(s):

Differential Equations ◽

Boundary Conditions ◽

Fractional Differential Equations ◽

Coupled System ◽

Contraction Mapping Principle ◽

Existence And Uniqueness Results ◽

Uniqueness Results ◽

Nonlinear Coupled System ◽

Coupled Boundary Conditions ◽

Fractional Differential

AbstractIn this research we introduce and study a new coupled system of three fractional differential equations supplemented with nonlocal multi-point coupled boundary conditions. Existence and uniqueness results are established by using the Leray–Schauder alternative and Banach’s contraction mapping principle. Illustrative examples are also presented.

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Existence and Uniqueness Results for a Coupled System of Nonlinear Fractional Differential Equations with Antiperiodic Boundary Conditions

Abstract and Applied Analysis ◽

10.1155/2014/463517 ◽

2014 ◽

Vol 2014 ◽

pp. 1-7

Author(s):

Huina Zhang ◽

Wenjie Gao

Keyword(s):

Differential Equations ◽

Boundary Conditions ◽

Fractional Differential Equations ◽

Existence And Uniqueness ◽

Coupled System ◽

Uniqueness Of Solutions ◽

Nonlinear Fractional Differential Equations ◽

Uniqueness Results ◽

Nonlinear Alternative ◽

Fractional Differential

This paper studies the existence and uniqueness of solutions for a coupled system of nonlinear fractional differential equations of orderα,β∈(4,5]with antiperiodic boundary conditions. Our results are based on the nonlinear alternative of Leray-Schauder type and the contraction mapping principle. Two illustrative examples are also presented.

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A Langevin-Type q-Variant System of Nonlinear Fractional Integro-Difference Equations with Nonlocal Boundary Conditions

Fractal and Fractional ◽

10.3390/fractalfract6010045 ◽

2022 ◽

Vol 6 (1) ◽

pp. 45

Author(s):

Ravi P. Agarwal ◽

Hana Al-Hutami ◽

Bashir Ahmad

Keyword(s):

Boundary Conditions ◽

Difference Equations ◽

Nonlocal Boundary ◽

Nonlocal Boundary Conditions ◽

Existence And Uniqueness Results ◽

New Class ◽

Uniqueness Results ◽

Multipoint Boundary Conditions ◽

The Given ◽

Variant System

We introduce a new class of boundary value problems consisting of a q-variant system of Langevin-type nonlinear coupled fractional integro-difference equations and nonlocal multipoint boundary conditions. We make use of standard fixed-point theorems to derive the existence and uniqueness results for the given problem. Illustrative examples for the obtained results are also presented.

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

Symmetry ◽

10.3390/sym13112212 ◽

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.

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On the Nonlocal Fractional Delta-Nabla Sum Boundary Value Problem for Sequential Fractional Delta-Nabla Sum-Difference Equations

Mathematics ◽

10.3390/math8040476 ◽

2020 ◽

Vol 8 (4) ◽

pp. 476

Author(s):

Jiraporn Reunsumrit ◽

Thanin Sitthiwirattham

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Boundary Value Problem ◽

Boundary Conditions ◽

Difference Equations ◽

Existence And Uniqueness ◽

Existence And Uniqueness Results ◽

Uniqueness Results ◽

Banach Contraction ◽

The Banach Contraction Principle

In this paper, we propose sequential fractional delta-nabla sum-difference equations with nonlocal fractional delta-nabla sum boundary conditions. The Banach contraction principle and the Schauder’s fixed point theorem are used to prove the existence and uniqueness results of the problem. The different orders in one fractional delta differences, one fractional nabla differences, two fractional delta sum, and two fractional nabla sum are considered. Finally, we present an illustrative example.

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Non-Instantaneous Impulsive Boundary Value Problems Containing Caputo Fractional Derivative of a Function with Respect to Another Function and Riemann–Stieltjes Fractional Integral Boundary Conditions

Axioms ◽

10.3390/axioms10030130 ◽

2021 ◽

Vol 10 (3) ◽

pp. 130

Author(s):

Suphawat Asawasamrit ◽

Yasintorn Thadang ◽

Sotiris K. Ntouyas ◽

Jessada Tariboon

Keyword(s):

Boundary Conditions ◽

Fractional Derivative ◽

Boundary Value Problems ◽

Caputo Fractional Derivative ◽

Fractional Integral ◽

Boundary Value ◽

Integral Boundary Conditions ◽

Integral Boundary ◽

Uniqueness Results ◽

Nonlinear Alternative

In the present article we study existence and uniqueness results for a new class of boundary value problems consisting by non-instantaneous impulses and Caputo fractional derivative of a function with respect to another function, supplemented with Riemann–Stieltjes fractional integral boundary conditions. The existence of a unique solution is obtained via Banach’s contraction mapping principle, while an existence result is established by using Leray–Schauder nonlinear alternative. Examples illustrating the main results are also constructed.

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A Self-Adjoint Coupled System of Nonlinear Ordinary Differential Equations with Nonlocal Multi-Point Boundary Conditions on an Arbitrary Domain

Applied Sciences ◽

10.3390/app11114798 ◽

2021 ◽

Vol 11 (11) ◽

pp. 4798

Author(s):

Hari Mohan Srivastava ◽

Sotiris K. Ntouyas ◽

Mona Alsulami ◽

Ahmed Alsaedi ◽

Bashir Ahmad

Keyword(s):

Differential Equations ◽

Boundary Conditions ◽

Ordinary Differential Equations ◽

Coupled System ◽

Contraction Mapping Principle ◽

Arbitrary Domain ◽

Banach Contraction ◽

Coupled Boundary Conditions ◽

Banach Contraction Mapping Principle ◽

Banach Contraction Mapping

The main object of this paper is to investigate the existence of solutions for a self-adjoint coupled system of nonlinear second-order ordinary differential equations equipped with nonlocal multi-point coupled boundary conditions on an arbitrary domain. We apply the Leray–Schauder alternative, the Schauder fixed point theorem and the Banach contraction mapping principle in order to derive the main results, which are then well-illustrated with the aid of several examples. Some potential directions for related further researches are also indicated.

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Some Proximal Methods for Solving Mixed Variational Inequalities

Abstract and Applied Analysis ◽

10.1155/2012/610852 ◽

2012 ◽

Vol 2012 ◽

pp. 1-9

Author(s):

Muhammad Aslam Noor ◽

Zhenyu Huang

Keyword(s):

Variational Inequalities ◽

Extragradient Method ◽

Fixed Point Problem ◽

Point Problem ◽

Proximal Methods ◽

Proximal Point ◽

Equivalent Formulation ◽

New Methods ◽

Special Cases ◽

Mixed Variational Inequalities

It is well known that the mixed variational inequalities are equivalent to the fixed point problem. We use this alternative equivalent formulation to suggest some new proximal point methods for solving the mixed variational inequalities. These new methods include the explicit, the implicit, and the extragradient method as special cases. The convergence analysis of these new methods is considered under some suitable conditions. Our method of constructing these iterative methods is very simple. Results proved in this paper may stimulate further research in this direction.

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