scholarly journals An Iterative Algorithm for Solving n -Order Fractional Differential Equation with Mixed Integral and Multipoint Boundary Conditions

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Jingjing Tan ◽  
Xinguang Zhang ◽  
Lishan Liu ◽  
Yonghong Wu
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Positive Solution ◽  
Fractional Differential Equation ◽  
Iterative Algorithm ◽  
Iterative Scheme ◽  
Approximation Error ◽  
Multipoint Boundary ◽  
Multipoint Boundary Conditions ◽  
Fractional Differential

In this paper, we consider the iterative algorithm for a boundary value problem of n -order fractional differential equation with mixed integral and multipoint boundary conditions. Using an iterative technique, we derive an existence result of the uniqueness of the positive solution, then construct the iterative scheme to approximate the positive solution of the equation, and further establish some numerical results on the estimation of the convergence rate and the approximation error.

scholarly journals Uniqueness of Iterative Positive Solution to Nonlinear Fractional Differential Equations with Negatively Perturbed Term

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Jingjing Tan ◽  
Meixia Li ◽  
Aixia Pan
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Convergence Rate ◽  
Boundary Value Problem ◽  
Positive Solution ◽  
Fractional Differential Equation ◽  
Fractional Differential Equations ◽  
Iterative Scheme ◽  
Approximation Error ◽  
Fractional Differential

We prove that there are unique positive solutions for a new kind of fractional differential equation with a negatively perturbed term boundary value problem. Our methods rely on an iterative algorithm which requires constructing an iterative scheme to approximate the solution. This allows us to calculate the estimation of the convergence rate and the approximation error.

scholarly journals Implicit fractional differential equation with nonlocal integral-multipoint boundary conditions in the frame of Hilfer fractional derivative

2021 ◽  
Vol 2 (1) ◽  
pp. 62-71
Author(s):  
Saleh Redhwan ◽  
Sadikali L. Shaikh
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Fractional Derivative ◽  
Fractional Differential Equation ◽  
Hilfer Fractional Derivative ◽  
Multipoint Boundary ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Multipoint Boundary Conditions ◽  
Fractional Differential

This article deals with a nonlinear implicit fractional differential equation with nonlocal integral-multipoint boundary conditions in the frame of Hilfer fractional derivative. The existence and uniqueness results are obtained by using the fixed point theorems of Krasnoselskii and Banach. Further, to demonstrate the effectiveness of the main results, suitable examples are granted.

scholarly journals Positive Solutions for the Eigenvalue Problem of Semipositone Fractional Order Differential Equation with Multipoint Boundary Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Ge Dong
Keyword(s):  
Differential Equation ◽  
Eigenvalue Problem ◽  
Boundary Conditions ◽  
Positive Solution ◽  
Fractional Order ◽  
Order Differential Equation ◽  
Sufficient Conditions ◽  
Fractional Order Differential Equation ◽  
Multipoint Boundary ◽  
Multipoint Boundary Conditions

We study the existence of positive solution for the eigenvalue problem of semipositone fractional order differential equation with multipoint boundary conditions by using known Krasnosel'skii's fixed point theorem. Some sufficient conditions that guarantee the existence of at least one positive solution for eigenvalues  λ>0sufficiently small andλ>0sufficiently large are established.

scholarly journals Positive Solution of Singular Fractional Differential Equation in Banach Space

2011 ◽  
Vol 2011 ◽  
pp. 1-22 ◽  
Author(s):  
Jianxin Cao ◽  
Haibo Chen
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Boundary Value Problem ◽  
Positive Solution ◽  
Fractional Differential Equation ◽  
Nonlinear Term ◽  
Existence Results ◽  
Multipoint Boundary ◽  
Fractional Differential ◽  
Multipoint Boundary Value Problem

We investigated a singular multipoint boundary value problem for fractional differential equation in Banach space. The nonlinear term is positive and singular at and (or) . Employing regularization, sequential techniques, and diagonalization methods, we obtained some new existence results of positive solution.

scholarly journals On a nonlinear system of Riemann-Liouville fractional differential equations with semi-coupled integro-multipoint boundary conditions

2021 ◽  
Vol 19 (1) ◽  
pp. 760-772
Author(s):  
Ahmed Alsaedi ◽  
Bashir Ahmad ◽  
Badrah Alghamdi ◽  
Sotiris K. Ntouyas
Keyword(s):  
Nonlinear System ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Numerical Examples ◽  
Multipoint Boundary ◽  
Multipoint Boundary Conditions ◽  
Fractional Differential

Abstract We study a nonlinear system of Riemann-Liouville fractional differential equations equipped with nonseparated semi-coupled integro-multipoint boundary conditions. We make use of the tools of the fixed-point theory to obtain the desired results, which are well-supported with numerical examples.

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