scholarly journals A New Impulsive Multi-Orders Fractional Differential Equation Involving Multipoint Fractional Integral Boundary Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Guotao Wang ◽  
Sanyang Liu ◽  
Dumitru Baleanu ◽  
Lihong Zhang
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Fractional Differential Equation ◽  
Fractional Integral ◽  
Fixed Point Theorems ◽  
Integral Boundary Conditions ◽  
Integral Boundary ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Fractional Differential

A new impulsive multi-orders fractional differential equation is studied. The existence and uniqueness results are obtained for a nonlinear problem with fractional integral boundary conditions by applying standard fixed point theorems. An example for the illustration of the main result is presented.

scholarly journals Analysis of implicit type of a generalized fractional differential equations with nonlinear integral boundary conditions

2020 ◽  
Vol 1 (1) ◽  
pp. 64-76
Author(s):  
Saleh Redhwan ◽  
Sadikali Shaikh
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Integral Boundary Conditions ◽  
Integral Boundary ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Fractional Differential ◽  
The Given

The given paper describes the implicit fractional differential equation with nonlinear integral boundary conditions in the frame of Caputo-Katugampola fractional derivative. We obtain an analogous integral equation of the given problem and prove the existence and uniqueness results of such a problem using the Banach and Krasnoselskii fixed point theorems. To show the effectiveness of the acquired results, convenient examples are presented.

scholarly journals Positive Solutions for Boundary Value Problems of Fractional Differential Equation with Integral Boundary Conditions

2018 ◽  
Vol 2018 ◽  
pp. 1-6 ◽  
Author(s):  
Qiao Sun ◽  
Hongwei Ji ◽  
Yujun Cui
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Fractional Differential Equation ◽  
Positive Solutions ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Integral Boundary Conditions ◽  
Existence Results ◽  
Integral Boundary ◽  
Fractional Differential

By using two fixed-point theorems on cone, we discuss the existence results of positive solutions for the following boundary value problem of fractional differential equation with integral boundary conditions: D0+αx(t)+a(t)f(t,x(t))=0, t∈(0,1), x(0)=x′(0)=0, and x(1)=∫01x(t)dA(t).

scholarly journals On a Hilfer fractional differential equation with nonlocal Erdélyi-Kober fractional integral boundary conditions

Filomat ◽  
2020 ◽  
Vol 34 (9) ◽  
pp. 3003-3014
Author(s):  
Mohamed Abbas
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Conditions ◽  
Fractional Differential Equation ◽  
Point Theorem ◽  
Fractional Integral ◽  
Integral Boundary Conditions ◽  
Integral Boundary ◽  
Fractional Differential

We consider a Hilfer fractional differential equation with nonlocal Erd?lyi-Kober fractional integral boundary conditions. The existence, uniqueness and Ulam-Hyers stability results are investigated by means of the Krasnoselskii?s fixed point theorem and Banach?s fixed point theorem. An example is given to illustrate the main results.

scholarly journals Positive Solutions for BVP of Fractional Differential Equation with Integral Boundary Conditions

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Min Li ◽  
Jian-Ping Sun ◽  
Ya-Hong Zhao
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Fractional Differential Equation ◽  
Positive Solutions ◽  
Integral Boundary Conditions ◽  
Monotone Iterative Method ◽  
Nonlinear Fractional Differential Equation ◽  
Integral Boundary ◽  
Zero Function ◽  
Fractional Differential

In this paper, we consider a class of boundary value problems of nonlinear fractional differential equation with integral boundary conditions. By applying the monotone iterative method and some inequalities associated with Green’s function, we obtain the existence of minimal and maximal positive solutions and establish two iterative sequences for approximating the solutions to the above problem. It is worth mentioning that these iterative sequences start off with zero function or linear function, which is useful and feasible for computational purpose. An example is also included to illustrate the main result of this paper.

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