scholarly journals Existence and uniqueness of solutions for a coupled system of nonlinear fractional differential equations with fractional integral boundary conditions

2016 ◽  
Vol 09 (05) ◽  
pp. 2434-2447 ◽  
Author(s):  
Haiyan Zhang ◽  
Yaohong Li ◽  
Wei Lu
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Fractional Integral ◽  
Integral Boundary Conditions ◽  
Coupled System ◽  
Uniqueness Of Solutions ◽  
Integral Boundary ◽  
Fractional Differential

scholarly journals Existence and Uniqueness Results for Hadamard-Type Fractional Differential Equations with Nonlocal Fractional Integral Boundary Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Phollakrit Thiramanus ◽  
Sotiris K. Ntouyas ◽  
Jessada Tariboon
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Fractional Integral ◽  
Integral Boundary Conditions ◽  
Uniqueness Of Solutions ◽  
Integral Boundary ◽  
Uniqueness Results ◽  
Fractional Differential

We study the existence and uniqueness of solutions for a fractional boundary value problem involving Hadamard-type fractional differential equations and nonlocal fractional integral boundary conditions. Our results are based on some classical fixed point theorems. Some illustrative examples are also included.

scholarly journals On Coupledp-Laplacian Fractional Differential Equations with Nonlinear Boundary Conditions

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Aziz Khan ◽  
Yongjin Li ◽  
Kamal Shah ◽  
Tahir Saeed Khan
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Integral Boundary Conditions ◽  
Coupled System ◽  
Laplacian Operator ◽  
Uniqueness Of Solutions ◽  
Integral Boundary ◽  
Fractional Differential

This paper is related to the existence and uniqueness of solutions to a coupled system of fractional differential equations (FDEs) with nonlinearp-Laplacian operator by using fractional integral boundary conditions with nonlinear term and also to checking the Hyers-Ulam stability for the proposed problem. The functions involved in the proposed coupled system are continuous and satisfy certain growth conditions. By using topological degree theory some conditions are established which ensure the existence and uniqueness of solution to the proposed problem. Further, certain conditions are developed corresponding to Hyers-Ulam type stability for the positive solution of the considered coupled system of FDEs. Also, from applications point of view, we give an example.

scholarly journals Existence and Uniqueness Results for a Coupled System of Caputo-Hadamard Fractional Differential Equations with Nonlocal Hadamard Type Integral Boundary Conditions

2020 ◽  
Vol 4 (2) ◽  
pp. 13 ◽  
Author(s):  
Shorog Aljoudi ◽  
Bashir Ahmad ◽  
Ahmed Alsaedi
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Nonlocal Boundary ◽  
Integral Boundary Conditions ◽  
Coupled System ◽  
Integral Boundary ◽  
Uniqueness Results ◽  
Fractional Differential

In this paper, we study a coupled system of Caputo-Hadamard type sequential fractional differential equations supplemented with nonlocal boundary conditions involving Hadamard fractional integrals. The sufficient criteria ensuring the existence and uniqueness of solutions for the given problem are obtained. We make use of the Leray-Schauder alternative and contraction mapping principle to derive the desired results. Illustrative examples for the main results are also presented.

scholarly journals Boundary value problems for Hilfer fractional differential equations with Katugampola fractional integral and anti-periodic conditions

Mathematica ◽  
2021 ◽  
Vol 63 (86) (2) ◽  
pp. 208-221
Author(s):  
Abdelatif Boutiara ◽  
◽  
Maamar Benbachir ◽  
Kaddour Guerbati ◽  
◽  
...  
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Fractional Integral ◽  
Integral Boundary Conditions ◽  
General Nature ◽  
Uniqueness Of Solutions ◽  
Integral Boundary ◽  
Special Cases ◽  
Fractional Differential

The purpose of this paper is to investigate the existence and uniqueness of solutions for a new class of nonlinear fractional differential equations involving Hilfer fractional operator with fractional integral boundary conditions. Our analysis relies on classical fixed point theorems and the Boyd-Wong nonlinear contraction. At the end, an illustrative example is presented. The boundary conditions introduced in this work are of quite general nature and can be reduce to many special cases by fixing the parameters involved in the conditions.

scholarly journals Existence and Uniqueness Results for Fractional Differential Equations with Riemann-Liouville Fractional Integral Boundary Conditions

2015 ◽  
Vol 2015 ◽  
pp. 1-6
Author(s):  
Mohamed I. Abbas
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Fractional Integral ◽  
Integral Boundary Conditions ◽  
Uniqueness Result ◽  
Integral Boundary ◽  
Uniqueness Results ◽  
Fractional Differential

We prove the existence and uniqueness of solution for fractional differential equations with Riemann-Liouville fractional integral boundary conditions. The first existence and uniqueness result is based on Banach’s contraction principle. Moreover, other existence results are also obtained by using the Krasnoselskii fixed point theorem. An example is given to illustrate the main results.

scholarly journals Boundary value problems for Caputo fractional differential equations with nonlocal and fractional integral boundary conditions

2020 ◽  
Vol 9 (3) ◽  
pp. 531-544
Author(s):  
Choukri Derbazi ◽  
Hadda Hammouche
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Fractional Integral ◽  
Integral Boundary Conditions ◽  
Integral Boundary ◽  
Uniqueness Results ◽  
Fractional Differential

Abstract In this paper, we study the existence and uniqueness of solutions for fractional differential equations with nonlocal and fractional integral boundary conditions. New existence and uniqueness results are established using the Banach contraction principle. Other existence results are obtained using O’Regan fixed point theorem and Burton and Kirk fixed point. In addition, an example is given to demonstrate the application of our main results.

A fully Hadamard type integral boundary value problem of a coupled system of fractional differential equations

2014 ◽  
Vol 17 (2) ◽  
Author(s):  
Bashir Ahmad ◽  
Sotiris Ntouyas
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Integral Boundary Conditions ◽  
Coupled System ◽  
Uniqueness Of Solutions ◽  
Integral Boundary ◽  
Type Integral ◽  
Fractional Differential

AbstractThis paper is concerned with the existence and uniqueness of solutions for a coupled system of Hadamard type fractional differential equations and integral boundary conditions. We emphasize that much work on fractional boundary value problems involves either Riemann-Liouville or Caputo type fractional differential equations. In the present work, we have considered a new problem which deals with a system of Hadamard differential equations and Hadamard type integral boundary conditions. The existence of solutions is derived from Leray-Schauder’s alternative, whereas the uniqueness of solution is established by Banach’s contraction principle. An illustrative example is also included.

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