scholarly journals On singular systems of nonlinear equations involving 3n-Caputo derivatives

2020 ◽  
Vol 23 (2) ◽  
pp. 179-192
Author(s):  
Amele Taïeb
Keyword(s):  
Existence And Uniqueness ◽  
Contraction Mapping ◽  
Singular Systems ◽  
Nonlinear Differential Equations ◽  
Contraction Mapping Principle ◽  
Systems Of Nonlinear Equations ◽  
Fractional Systems ◽  
Caputo Derivatives ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results

We study singular fractional systems of nonlinear differential equations involving 3n-Caputo derivatives. We investigate existence and uniqueness results using the contraction mapping principle. We also discuss the existence of at least one solution by means of Schauder fixed point theorem. Moreover, we define and discuss the Ulam–Hyers stability and the generalized Ulam–Hyers stability of solutions for such systems. To illustrate the main results, we present some examples.

scholarly journals Existence and uniqueness results for Ψ-fractional integro-differential equations with boundary conditions

2020 ◽  
Vol 107 (121) ◽  
pp. 145-155
Author(s):  
Devaraj Vivek ◽  
E.M. Elsayed ◽  
Kuppusamy Kanagarajan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Derivative ◽  
Existence And Uniqueness ◽  
Contraction Mapping ◽  
Contraction Mapping Principle ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results

We study boundary value problems (BVPs for short) for the integro- differential equations via ?-fractional derivative. The results are obtained by using the contraction mapping principle and Schaefer?s fixed point theorem. In addition, we discuss the Ulam-Hyers stability.

scholarly journals SHARPER EXISTENCE AND UNIQUENESS RESULTS FOR SOLUTIONS TO THIRD-ORDER BOUNDARY VALUE PROBLEMS

2020 ◽  
Vol 25 (3) ◽  
pp. 409-420 ◽  
Author(s):  
Saleh S. Almuthaybiri ◽  
Christopher C. Tisdell
Keyword(s):  
Boundary Value Problems ◽  
Existence And Uniqueness ◽  
Contraction Mapping ◽  
Boundary Value ◽  
Uniqueness Of Solutions ◽  
Third Order ◽  
Contraction Mapping Theorem ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Banach’S Fixed Point Theorem

The purpose of this note is to sharpen Smirnov’s recent work on existence and uniqueness of solutions to third-order ordinary differential equations that are subjected to two- and three-point boundary conditions. The advancement is achieved in the following ways. Firstly, we provide sharp and sharpened estimates for integrals regarding various Green’s functions. Secondly, we apply these sharper estimates to problems in conjunction with Banach’s fixed point theorem. Thirdly, we apply Rus’s contraction mapping theorem in a metric space, where two metrics are employed. Our new results improve those of Smirnov by showing that a larger class of boundary value problems admit a unique solution.

scholarly journals Quantum Difference Langevin System with Nonlocalq-Derivative Conditions

2016 ◽  
Vol 2016 ◽  
pp. 1-11
Author(s):  
Surang Sitho ◽  
Sorasak Laoprasittichok ◽  
Sotiris K. Ntouyas ◽  
Jessada Tariboon
Keyword(s):  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Contraction Mapping Principle ◽  
Coupled Systems ◽  
Uniqueness Of Solutions ◽  
Existence And Uniqueness Results ◽  
New Class ◽  
Uniqueness Results ◽  
Difference Systems ◽  
Quantum Difference

We introduce a new class of boundary value problems for Langevin quantum difference systems. Some new existence and uniqueness results for coupled systems are obtained by using fixed point theorems. The existence and uniqueness of solutions are established by Banach’s contraction mapping principle, while the existence of solutions is derived by using Leray-Schauder’s alternative. The obtained results are well illustrated with the aid of examples.

scholarly journals Solvability for Discrete Fractional Boundary Value Problems with ap-Laplacian Operator

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Weidong Lv
Keyword(s):  
Contraction Mapping ◽  
Boundary Value ◽  
Contraction Mapping Principle ◽  
Laplacian Operator ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Banach Contraction ◽  
Banach Contraction Mapping Principle ◽  
Fractional Boundary Value Problems ◽  
Banach Contraction Mapping

This paper is concerned with the solvability for a discrete fractionalp-Laplacian boundary value problem. Some existence and uniqueness results are obtained by means of the Banach contraction mapping principle. Additionally, two representative examples are presented to illustrate the effectiveness of the main results.

scholarly journals Analysis of 2 + 1 diffusive–dispersive PDE arising in river braiding

2016 ◽  
Vol 27 (5) ◽  
pp. 756-780
Author(s):  
SALEH TANVEER ◽  
CHARIS TSIKKOU
Keyword(s):  
Boundary Condition ◽  
Existence And Uniqueness ◽  
Contraction Mapping ◽  
Local Existence ◽  
Dispersive Equation ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Local Existence And Uniqueness ◽  
Formula Group ◽  
Image Position

We present local existence and uniqueness results for the following 2 + 1 diffusive–dispersive equation due to P. Hall arising in modelling of river braiding: $$\begin{equation*} u_{yyt} - \gamma u_{xxx} -\alpha u_{yyyy} - \beta u_{yy} + \left ( u^2 \right )_{xyy} = 0 \end{equation*}$$ for (x,y) ∈ [0, 2π] × [0, π], t > 0, with boundary condition uy=0=uyyy at y=0 and y=π and 2π periodicity in x, using a contraction mapping argument in a Bourgain-type space Ts,b. We also show that the energy ∥u(·, ·, t)∥2L2 and cumulative dissipation ∫0t∥uy (·, ·, s)∥L22dt are globally controlled in time t.

scholarly journals New Existence of Solutions for Fractional Integro-Differential Equations with Nonseparated Boundary Conditions

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Lahcen Ibnelazyz ◽  
Karim Guida ◽  
Khalid Hilal ◽  
Said Melliani
Keyword(s):  
Differential Equations ◽  
Existence And Uniqueness ◽  
Contraction Mapping ◽  
Existence Of Solutions ◽  
Contraction Mapping Principle ◽  
Existence Of Solution ◽  
Uniqueness Of Solutions ◽  
Uniqueness Results ◽  
Nonseparated Boundary Conditions ◽  
Krasnoselskii Fixed Point Theorem

Results reported in this article prove the existence and uniqueness of solutions for a class of nonlinear fractional integro-differential equations supplemented by nonseparated boundary value conditions. We consider a new norm to establish the existence of solution via Krasnoselskii fixed point theorem; however, the uniqueness results are obtained by applying the contraction mapping principle. Some examples are provided to illustrate the results.

scholarly journals Existence and Uniqueness of Solution to Nonlinear Boundary Value Problems with Sign-Changing Green’s Function

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Peiguo Zhang ◽  
Lishan Liu ◽  
Yonghong Wu
Keyword(s):  
Green’S Function ◽  
Boundary Value Problems ◽  
Green's Function ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Contraction Mapping Principle ◽  
Nonlinear Boundary Value Problems ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Equation Boundary

By using the cone theory and the Banach contraction mapping principle, the existence and uniqueness results are established for nonlinear higher-order differential equation boundary value problems with sign-changing Green’s function. The theorems obtained are very general and complement previous known results.

scholarly journals Existence Results for Impulsive Fractional q-Difference Equation with Antiperiodic Boundary Conditions

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Mingyue Zuo ◽  
Xinan Hao
Keyword(s):  
Difference Equation ◽  
Contraction Mapping ◽  
Contraction Mapping Principle ◽  
Existence Results ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Nonlinear Alternative ◽  
Banach Contraction ◽  
Banach Contraction Mapping Principle ◽  
Banach Contraction Mapping

In this paper, we investigate the impulsive fractional q-difference equation with antiperiodic conditions. The existence and uniqueness results of solutions are established via the theorem of nonlinear alternative of Leray-Schauder type and the Banach contraction mapping principle. Two examples are given to illustrate our results.

scholarly journals Existence and uniqueness results for the first-order non-linear impulsive integro-differential equations with two-point boundary conditions

2021 ◽  
Vol 102 (2) ◽  
pp. 74-83
Author(s):  
M.J. Mardanov ◽  
◽  
R.S. Mammadov ◽  
S.Yu. Gasimov ◽  
Ya.A. Sharifov ◽  
...  
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Existence And Uniqueness ◽  
Contraction Mapping Principle ◽  
Point Boundary ◽  
Uniqueness Of Solutions ◽  
First Order ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
The Green Function

The article discusses the existence and uniqueness of solutions for a system of nonlinear integro-differential equations of the first order with two-point boundary conditions. The Green function is constructed, and the problem under consideration is reduced to equivalent integral equation. Existence and uniqueness of a solution to this problem is analyzed using the Banach contraction mapping principle. Schaefer’s fixed point theorem is used to prove the existence of solutions.

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