scholarly journals Existence and Uniqueness Theorems for Impulsive Fractional Differential Equations with the Two-Point and Integral Boundary Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
M. J. Mardanov ◽  
N. I. Mahmudov ◽  
Y. A. Sharifov
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Integral Boundary Conditions ◽  
Integral Boundary ◽  
Impulsive Fractional Differential Equations ◽  
Fractional Differential ◽  
Uniqueness Of A Solution

We study a boundary value problem for the system of nonlinear impulsive fractional differential equations of orderα  0<α≤1involving the two-point and integral boundary conditions. Some new results on existence and uniqueness of a solution are established by using fixed point theorems. Some illustrative examples are also presented. We extend previous results even in the integer caseα=1.

scholarly journals Positive solutions for generalized two-term fractional differential equations with integral boundary conditions

2020 ◽  
Vol 1 (1) ◽  
pp. 47-63
Author(s):  
Hanan A. Wahash ◽  
Satish K. Panchal
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Upper And Lower Solutions ◽  
Integral Boundary Conditions ◽  
Integral Boundary ◽  
Fractional Differential

In this paper, we consider a class of boundary value problems for nonlinear two-term fractional differential equations with integral boundary conditions involving two $\psi $-Caputo fractional derivative. With the help of the properties Green function, the fixed point theorems of Schauder and Banach, and the method of upper and lower solutions, we derive the existence and uniqueness of positive solution of a proposed problem. Finally, an example is provided to illustrate the acquired results.

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 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 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 the Existence of Solutions for Impulsive Fractional Differential Equations

2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Yongliang Guan ◽  
Zengqin Zhao ◽  
Xiuli Lin
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Positive Solution ◽  
Fractional Differential Equations ◽  
Existence Of Solutions ◽  
Global Bifurcation ◽  
Integral Boundary Conditions ◽  
Integral Boundary ◽  
Impulsive Fractional Differential Equations ◽  
Fractional Differential

We are concerned with a type of impulsive fractional differential equations attached with integral boundary conditions and get the existence of at least one positive solution via global bifurcation techniques.

scholarly journals Solutions for a category of singular nonlinear fractional differential equations subject to integral boundary conditions

2022 ◽  
Vol 2022 (1) ◽  
Author(s):  
Debao Yan
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Nonlinear Function ◽  
Integral Boundary Conditions ◽  
Singular Boundary ◽  
Integral Boundary ◽  
Fractional Differential ◽  
Uniqueness Of A Solution

AbstractWe concentrate on a category of singular boundary value problems of fractional differential equations with integral boundary conditions, in which the nonlinear function f is singular at $t=0$ t = 0 , 1. We use Banach’s fixed-point theorem and Hölder’s inequality to verify the existence and uniqueness of a solution. Moreover, also we prove the existence of solutions by Krasnoselskii’s and Schaefer’s fixed point theorems.

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.

Sign in / Sign up

Export Citation Format

Share Document