Monotone iterative technique for neutral fractional differential equation with infinite delay

2016 ◽  
Vol 39 (15) ◽  
pp. 4642-4653 ◽  
Author(s):  
Renu Chaudhary ◽  
Dwijendra N. Pandey
Keyword(s):  
Differential Equation ◽  
Fractional Differential Equation ◽  
Infinite Delay ◽  
Monotone Iterative Technique ◽  
Iterative Technique ◽  
Monotone Iterative ◽  
Fractional Differential

Monotone Iterative Technique for Periodic Boundary Value Problem of Fractional Differential Equation in Banach Spaces

2019 ◽  
Vol 20 (5) ◽  
pp. 595-599 ◽  
Author(s):  
Pengyu Chen ◽  
Yibo Kong
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Banach Spaces ◽  
Fractional Differential Equation ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Monotone Iterative Technique ◽  
Iterative Technique ◽  
Monotone Iterative ◽  
Fractional Differential

AbstractIn this paper, we are concerned with the periodic boundary value problem of fractional differential equations on ordered Banach spaces. By introducing a concept of upper and lower solutions, we construct a new monotone iterative technique for the periodic boundary value problems of fractional differential equation, and obtain the existence of solutions between lower and upper solutions.

Monotone iterative technique for impulsive Riemann-Liouville fractional differential equations

Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3381-3395 ◽  
Author(s):  
Renu Chaudhary ◽  
Dwijendra Pandey
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Measure Of Noncompactness ◽  
Semigroup Theory ◽  
Monotone Iterative Technique ◽  
Iterative Technique ◽  
Monotone Iterative ◽  
Fractional Differential

In this article, Monotone iterative technique coupled with the method of lower and upper solutions is employed to discuss the existence and uniqueness of mild solution to an impulsive Riemann-Liouville fractional differential equation. The results are obtained using the concept of measure of noncompactness, semigroup theory and generalized Gronwall inequality for fractional differential equations. At last, an example is given to illustrate the applications of the main results.

scholarly journals Monotone iterative technique for nonlinear differential equation of fractional order

2021 ◽  
Author(s):  
Zhengzhi Lu ◽  
Li Yongjun ◽  
Xiaoyan Shi
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Iteration Method ◽  
Existence Of Solution ◽  
Monotone Iterative Technique ◽  
Iterative Technique ◽  
Monotone Iteration ◽  
Monotone Iterative ◽  
Fractional Differential ◽  
The Fixed Point Theorem

In this paper, we mainly study the existence of solution of fractional differential equations. Firstly, the existence of the maxmum solution and minmum solution of the differential equation are proved by using the fixed point theorem and the monotone iteration method. Secondly, the existence of the solution of the original equation is proved by using the newly constructed differential equation. Finally, the application of the monotone iteration method is given through an example.

scholarly journals Monotone Iterative Method for ψ-Caputo Fractional Differential Equation with Nonlinear Boundary Conditions

2021 ◽  
Vol 5 (3) ◽  
pp. 81
Author(s):  
Zidane Baitiche ◽  
Choukri Derbazi ◽  
Jehad Alzabut ◽  
Mohammad Esmael Samei ◽  
Mohammed K. A. Kaabar ◽  
...  
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Fractional Differential Equation ◽  
Nonlinear Boundary ◽  
Upper And Lower Solutions ◽  
Nonlinear Boundary Conditions ◽  
Monotone Iterative Technique ◽  
Monotone Iterative Method ◽  
Monotone Iterative ◽  
Fractional Differential

The main contribution of this paper is to prove the existence of extremal solutions for a novel class of ψ-Caputo fractional differential equation with nonlinear boundary conditions. For this purpose, we utilize the well-known monotone iterative technique together with the method of upper and lower solutions. Finally, we provide an example along with graphical representations to confirm the validity of our main results.

Monotone iterative method for a class of nonlinear fractional differential equations

2012 ◽  
Vol 15 (2) ◽  
Author(s):  
Guotao Wang ◽  
Dumitru Baleanu ◽  
Lihong Zhang
Keyword(s):  
Differential Equations ◽  
Iterative Method ◽  
Fractional Differential Equations ◽  
Monotone Iterative Technique ◽  
Monotone Iterative Method ◽  
Iterative Technique ◽  
Nonlinear Fractional Differential Equations ◽  
Monotone Iterative ◽  
Liouville Fractional Derivative ◽  
Fractional Differential

AbstractBy applying the monotone iterative technique and the method of lower and upper solutions, this paper investigates the existence of extremal solutions for a class of nonlinear fractional differential equations, which involve the Riemann-Liouville fractional derivative D q x(t). A new comparison theorem is also build. At last, an example is given to illustrate our main results.

scholarly journals Monotone Iterative Technique for Conformable Fractional Differential Equations with Deviating Arguments

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Huiling Chen ◽  
Shuman Meng ◽  
Yujun Cui
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Sufficient Conditions ◽  
Monotone Iterative Technique ◽  
Extremal Solutions ◽  
Iterative Technique ◽  
Deviating Arguments ◽  
Comparison Principles ◽  
Monotone Iterative ◽  
Fractional Differential

This paper is concerned with the existence of extremal solutions for periodic boundary value problems for conformable fractional differential equations with deviating arguments. We first build two comparison principles for the corresponding linear equation with deviating arguments. With the help of new comparison principles, some sufficient conditions for the existence of extremal solutions are established by combining the method of lower and upper solutions and the monotone iterative technique. As an application, an example is presented to enrich the main results of this article.

scholarly journals The Exact Iterative Solution of Fractional Differential Equation with Nonlocal Boundary Value Conditions

2018 ◽  
Vol 2018 ◽  
pp. 1-6 ◽  
Author(s):  
Jinxiu Mao ◽  
Zengqin Zhao ◽  
Chenguang Wang
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Fractional Differential Equation ◽  
Nonlocal Boundary ◽  
Approximation Error ◽  
Iterative Solution ◽  
Stieltjes Integral ◽  
Iterative Technique ◽  
Integral Conditions ◽  
Fractional Differential

We deal with a singular nonlocal fractional differential equation with Riemann-Stieltjes integral conditions. The exact iterative solution is established under the iterative technique. The iterative sequences have been proved to converge uniformly to the exact solution, and estimation of the approximation error and the convergence rate have been derived. An example is also given to demonstrate the results.

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