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 A Note on Fractional Differential Equations with Fractional Separated Boundary Conditions

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Bashir Ahmad ◽  
Sotiris K. Ntouyas
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Existence And Uniqueness Results ◽  
New Class ◽  
Uniqueness Results ◽  
Separated Boundary Conditions ◽  
Fractional Differential

We consider a new class of boundary value problems of nonlinear fractional differential equations with fractional separated boundary conditions. A connection between classical separated and fractional separated boundary conditions is developed. Some new existence and uniqueness results are obtained for this class of problems by using standard fixed point theorems. Some illustrative examples are also discussed.

scholarly journals Existence and uniqueness results for Φ-Caputo implicit fractional pantograph differential equation with generalized anti-periodic boundary condition

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Idris Ahmed ◽  
Poom Kumam ◽  
Thabet Abdeljawad ◽  
Fahd Jarad ◽  
Piyachat Borisut ◽  
...  
Keyword(s):  
Differential Equation ◽  
Green’S Function ◽  
Green's Function ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Uniqueness Of Solutions ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Special Cases ◽  
Generalized Fractional Derivative

Abstract The present paper describes the implicit fractional pantograph differential equation in the context of generalized fractional derivative and anti-periodic conditions. We formulated the Green’s function of the proposed problems. With the aid of a Green’s function, we obtain an analogous integral equation of the proposed problems and demonstrate the existence and uniqueness of solutions using the techniques of the Schaefer and Banach fixed point theorems. Besides, some special cases that show the proposed problems extend the current ones in the literature are presented. Finally, two examples were given as an application to illustrate the results obtained.

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.

scholarly journals Multi-term fractional differential equations with nonlocal boundary conditions

2018 ◽  
Vol 16 (1) ◽  
pp. 1519-1536
Author(s):  
Bashir Ahmad ◽  
Najla Alghamdi ◽  
Ahmed Alsaedi ◽  
Sotiris K. Ntouyas
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Fractional Differential ◽  
The Given

AbstractWe introduce and study a new kind of nonlocal boundary value problems of multi-term fractional differential equations. The existence and uniqueness results for the given problem are obtained by applying standard fixed point theorems. We also construct some examples for demonstrating the application of the main results.

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 On Caputo–Riemann–Liouville Type Fractional Integro-Differential Equations with Multi-Point Sub-Strip Boundary Conditions

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1899
Author(s):  
Ahmed Alsaedi ◽  
Amjad F. Albideewi ◽  
Sotiris K. Ntouyas ◽  
Bashir Ahmad
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Liouville Type ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results

In this paper, we derive existence and uniqueness results for a nonlinear Caputo–Riemann–Liouville type fractional integro-differential boundary value problem with multi-point sub-strip boundary conditions, via Banach and Krasnosel’skii⏝’s fixed point theorems. Examples are included for the illustration of the obtained results.

Existence, Uniqueness and Stability of Implicit Switched Coupled Fractional Differential Equations of ψ$\boldsymbol{\psi}$-Hilfer Type

2020 ◽  
Vol 21 (3-4) ◽  
pp. 327-337 ◽  
Author(s):  
Manzoor Ahmad ◽  
Akbar Zada ◽  
Xiaoming Wang
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Ulam Stability ◽  
Uniqueness Of Solutions ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Fractional Differential System ◽  
Fractional Differential ◽  
Fixed Point Techniques ◽  
Rassias Stability

AbstractIn this article, we study the existence and uniqueness of solutions of a switched coupled implicit ψ-Hilfer fractional differential system. The existence and uniqueness results are obtained by using fixed point techniques. Further, we investigate different kinds of stability such as Hyers–Ulam stability and Hyers–Ulam–Rassias stability. Finally, an example is provided to illustrate the obtained results.

scholarly journals Implicit-Relation-Type Cyclic Contractive Mappings and Applications to Integral Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Hemant Kumar Nashine ◽  
Zoran Kadelburg ◽  
Poom Kumam
Keyword(s):  
Integral Equations ◽  
Existence And Uniqueness ◽  
Contractive Condition ◽  
Uniqueness Of Solutions ◽  
Nonlinear Integral Equations ◽  
Implicit Relation ◽  
Existence And Uniqueness Results ◽  
Contractive Mappings ◽  
Uniqueness Results ◽  
Relation Type

We introduce an implicit-relation-type cyclic contractive condition for a map in a metric space and derive existence and uniqueness results of fixed points for such mappings. Examples are given to support the usability of our results. At the end of the paper, an application to the study of existence and uniqueness of solutions for a class of nonlinear integral equations is presented.

scholarly journals Existence and Uniqueness of Solutions for Coupled Impulsive Fractional Pantograph Differential Equations with Antiperiodic Boundary Conditions

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Karim Guida ◽  
Lahcen Ibnelazyz ◽  
Khalid Hilal ◽  
Said Melliani
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Differential Equations ◽  
Existence And Uniqueness ◽  
Uniqueness Of Solutions ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Fractional Differential ◽  
Banach’S Contraction Principle

In this paper, we investigate the solutions of coupled fractional pantograph differential equations with instantaneous impulses. The work improves some existing results and contributes toward the development of the fractional differential equation theory. We first provide some definitions that will be used throughout the paper; after that, we give the existence and uniqueness results that are based on Banach’s contraction principle and Krasnoselskii’s fixed point theorem. Two examples are given in the last part to support our study.

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