scholarly journals Existence Results for a Nonlocal Coupled System of Differential Equations Involving Mixed Right and Left Fractional Derivatives and Integrals

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 578
Author(s):  
Sotiris K. Ntouyas ◽  
Abrar Broom ◽  
Ahmed Alsaedi ◽  
Tareq Saeed ◽  
Bashir Ahmad
Keyword(s):  
Existence And Uniqueness ◽  
Fractional Derivatives ◽  
Fixed Point Theorems ◽  
Coupled System ◽  
Uniqueness Result ◽  
Existence Results ◽  
System Of Differential Equations ◽  
Liouville Type ◽  
Uniqueness Of Solutions ◽  
Fractional Derivatives And Integrals

In this paper, we study the existence and uniqueness of solutions for a new kind of nonlocal four-point fractional integro-differential system involving both left Caputo and right Riemann–Liouville fractional derivatives, and Riemann–Liouville type mixed integrals. The Banach and Schaefer fixed point theorems are used to obtain the desired results. An example illustrating the existence and uniqueness result is presented.

scholarly journals Stability Analysis and Existence of Solutions for a Modified SIRD Model of COVID-19 with Fractional Derivatives

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1431
Author(s):  
Bilal Basti ◽  
Nacereddine Hammami ◽  
Imadeddine Berrabah ◽  
Farid Nouioua ◽  
Rabah Djemiat ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Existence And Uniqueness ◽  
Fractional Derivatives ◽  
Fixed Point Theorems ◽  
Existence Of Solutions ◽  
Biological Models ◽  
Uniqueness Of Solutions ◽  
Caputo Fractional Derivatives ◽  
Single Form ◽  
Stability Results

This paper discusses and provides some analytical studies for a modified fractional-order SIRD mathematical model of the COVID-19 epidemic in the sense of the Caputo–Katugampola fractional derivative that allows treating of the biological models of infectious diseases and unifies the Hadamard and Caputo fractional derivatives into a single form. By considering the vaccine parameter of the suspected population, we compute and derive several stability results based on some symmetrical parameters that satisfy some conditions that prevent the pandemic. The paper also investigates the problem of the existence and uniqueness of solutions for the modified SIRD model. It does so by applying the properties of Schauder’s and Banach’s fixed point theorems.

scholarly journals Existence of Solutions ofα∈(2,3]Order Fractional Three-Point Boundary Value Problems with Integral Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
N. I. Mahmudov ◽  
S. Unul
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Fractional Derivatives ◽  
Fixed Point Theorems ◽  
Existence Of Solutions ◽  
Point Boundary ◽  
Integral Conditions ◽  
Uniqueness Of Solutions ◽  
Fractional Differential ◽  
Derivatives Of

Existence and uniqueness of solutions forα∈(2,3]order fractional differential equations with three-point fractional boundary and integral conditions involving the nonlinearity depending on the fractional derivatives of the unknown function are discussed. The results are obtained by using fixed point theorems. Two examples are given to illustrate the results.

scholarly journals Some Existence Results for Systems of Impulsive Stochastic Differential Equations

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Sliman Mekki ◽  
Tayeb Blouhi ◽  
Juan J. Nieto ◽  
Abdelghani Ouahab
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Banach Spaces ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Sufficient Conditions ◽  
Existence Results ◽  
Impulsive Systems ◽  
Uniqueness Of Solutions

Abstract In this paper we study a class of impulsive systems of stochastic differential equations with infinite Brownian motions. Sufficient conditions for the existence and uniqueness of solutions are established by mean of some fixed point theorems in vector Banach spaces. An example is provided to illustrate the theory.

scholarly journals Analysis of Coupled System of Implicit Fractional Differential Equations Involving Katugampola–Caputo Fractional Derivative

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-11 ◽  
Author(s):  
Manzoor Ahmad ◽  
Jiqiang Jiang ◽  
Akbar Zada ◽  
Syed Omar Shah ◽  
Jiafa Xu
Keyword(s):  
Fractional Derivative ◽  
Caputo Fractional Derivative ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Sufficient Conditions ◽  
Coupled System ◽  
Uniqueness Of Solutions ◽  
Fractional Differential System ◽  
Fractional Differential ◽  
Implicit Fractional Differential Equations

In this paper, we study the existence and uniqueness of solutions to implicit the coupled fractional differential system with the Katugampola–Caputo fractional derivative. Different fixed-point theorems are used to acquire the required results. Moreover, we derive some sufficient conditions to guarantee that the solutions to our considered system are Hyers–Ulam stable. We also provided an example that explains our results.

scholarly journals A Study of Nonlinear Fractionalq-Difference Equations with Nonlocal Integral Boundary Conditions

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Ahmed Alsaedi ◽  
Bashir Ahmad ◽  
Hana Al-Hutami
Keyword(s):  
Fixed Point ◽  
Boundary Conditions ◽  
Difference Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Integral Boundary Conditions ◽  
Existence Results ◽  
Uniqueness Of Solutions ◽  
Integral Boundary ◽  
Nonlocal Integral Boundary Conditions

This paper is concerned with the existence and uniqueness of solutions for a boundary value problem of nonlinear fractionalq-difference equations with nonlocal integral boundary conditions. The existence results are obtained by applying some well-known fixed point theorems and illustrated with examples.

scholarly journals Existence Results for a Nonlocal Coupled System of Sequential Fractional Differential Equations Involving ψ -Hilfer Fractional Derivatives

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Athasit Wongcharoen ◽  
Sotiris K. Ntouyas ◽  
Phollakrit Wongsantisuk ◽  
Jessada Tariboon
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Fractional Derivatives ◽  
Coupled System ◽  
Uniqueness Result ◽  
Uniqueness Of Solutions ◽  
New Class ◽  
Multipoint Boundary Conditions ◽  
Fractional Differential ◽  
Sequential Fractional Differential Equations

In this article, we discuss the existence and uniqueness of solutions for a new class of coupled system of sequential fractional differential equations involving ψ -Hilfer fractional derivatives, supplemented with multipoint boundary conditions. We make use of Banach’s fixed point theorem to obtain the uniqueness result and the Leray-Schauder alternative to obtain the existence result. Examples illustrating the main results are also constructed.

scholarly journals The generalized U–H and U–H stability and existence analysis of a coupled hybrid system of integro-differential IVPs involving φ-Caputo fractional operators

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Abdellatif Boutiara ◽  
Sina Etemad ◽  
Azhar Hussain ◽  
Shahram Rezapour
Keyword(s):  
Hybrid System ◽  
Coupled System ◽  
Uniqueness Result ◽  
Existence Results ◽  
Fractional Operators ◽  
Uniqueness Of Solutions ◽  
Banach Contraction ◽  
Hybrid Fixed Point Theorem ◽  
The Given ◽  
The Banach Contraction Principle

AbstractWe investigate the existence and uniqueness of solutions to a coupled system of the hybrid fractional integro-differential equations involving φ-Caputo fractional operators. To achieve this goal, we make use of a hybrid fixed point theorem for a sum of three operators due to Dhage and also the uniqueness result is obtained by making use of the Banach contraction principle. Moreover, we explore the Ulam–Hyers stability and its generalized version for the given coupled hybrid system. An example is presented to guarantee the validity of our existence results.

scholarly journals Investigation of the p-Laplacian nonperiodic nonlinear boundary value problem via generalized Caputo fractional derivatives

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
M. M. Matar ◽  
M. I. Abbas ◽  
J. Alzabut ◽  
M. K. A. Kaabar ◽  
S. Etemad ◽  
...  
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Fractional Derivatives ◽  
Fixed Point Theorems ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Nonlinear Boundary Value Problem ◽  
Uniqueness Of Solutions ◽  
Caputo Fractional Derivatives

AbstractA newly proposed p-Laplacian nonperiodic boundary value problem is studied in this research paper in the form of generalized Caputo fractional derivatives. The existence and uniqueness of solutions are fully investigated for this problem using some fixed point theorems such as Banach and Schauder. This work is supported with an example to apply all obtained new results and validate their applicability.

Existence and uniqueness of solutions for coupled systems of Liouville-Caputo type fractional integrodifferential equations with Erdélyi-Kober integral conditions

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Muthaiah Subramanian ◽  
Akbar Zada
Keyword(s):  
Fractional Derivatives ◽  
Integral Boundary Conditions ◽  
Coupled System ◽  
Uniqueness Result ◽  
Integrodifferential Equations ◽  
Coupled Systems ◽  
Uniqueness Of Solutions ◽  
Integral Boundary ◽  
Banach’S Fixed Point Theorem ◽  
The Given

AbstractIn this paper, we examine a coupled system of fractional integrodifferential equations of Liouville-Caputo form with nonlinearities depending on the unknown functions, as well as their lower-order fractional derivatives and integrals supplemented with coupled nonlocal and Erdélyi-Kober fractional integral boundary conditions. We explain that the topic discussed in this context is new and gives more analysis into the research of coupled boundary value problems. We have two results: the first is the existence result of the given problem by using the Leray-Schauder alternative, whereas the second referring to the uniqueness result is derived by Banach’s fixed-point theorem. Sufficient examples were also supplemented to substantiate the proof, and some variations of the problem were discussed.

scholarly journals Existence and Ulam–Hyers Stability of a Fractional-Order Coupled System in the Frame of Generalized Hilfer Derivatives

Mathematics ◽  
2021 ◽  
Vol 9 (20) ◽  
pp. 2543
Author(s):  
Abdulkafi M. Saeed ◽  
Mohammed S. Abdo ◽  
Mdi Begum Jeelani
Keyword(s):  
Fixed Point ◽  
Fractional Order ◽  
Existence And Uniqueness ◽  
Fractional Derivatives ◽  
Fixed Point Theorems ◽  
Coupled System ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Special Cases ◽  
Stability Of The Solution

In this research paper, we consider a class of a coupled system of fractional integrodifferential equations in the frame of Hilfer fractional derivatives with respect to another function. The existence and uniqueness results are obtained in weighted spaces by applying Schauder’s and Banach’s fixed point theorems. The results reported here are more general than those found in the literature, and some special cases are presented. Furthermore, we discuss the Ulam–Hyers stability of the solution to the proposed system. Some examples are also constructed to illustrate and validate the main results.

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