scholarly journals On a fractional problem of Lane–Emden type: Ulam type stabilities and numerical behaviors

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Kamel Tablennehas ◽  
Zoubir Dahmani ◽  
Meriem Mansouria Belhamiti ◽  
Amira Abdelnebi ◽  
Mehmet Zeki Sarikaya
Keyword(s):  
Differential Equation ◽  
Fractional Differential Equation ◽  
Caputo Derivative ◽  
Numerical Approach ◽  
Ulam Stability ◽  
Nonlinear Fractional Differential Equation ◽  
Fractional Differential

AbstractIn this work, we study some types of Ulam stability for a nonlinear fractional differential equation of Lane–Emden type with anti periodic conditions. Then, by using a numerical approach for the Caputo derivative, we investigate behaviors of the considered problem.

scholarly journals Positive Solution of a Nonlinear Fractional Differential Equation Involving Caputo Derivative

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Changyou Wang ◽  
Haiqiang Zhang ◽  
Shu Wang
Keyword(s):  
Differential Equation ◽  
Positive Solution ◽  
Fractional Differential Equation ◽  
Caputo Derivative ◽  
Nonlinear Term ◽  
Upper And Lower Solutions ◽  
Initial Value ◽  
Nonlinear Fractional Differential Equation ◽  
Control Functions ◽  
Fractional Differential

This paper is concerned with a nonlinear fractional differential equation involving Caputo derivative. By constructing the upper and lower control functions of the nonlinear term without any monotone requirement and applying the method of upper and lower solutions and the Schauder fixed point theorem, the existence and uniqueness of positive solution for the initial value problem are investigated. Moreover, the existence of maximal and minimal solutions is also obtained.

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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