The uniqueness of positive solution for a singular fractional differential system involving derivatives

2013 ◽  
Vol 18 (6) ◽  
pp. 1400-1409 ◽  
Author(s):  
Xinguang Zhang ◽  
Lishan Liu ◽  
Yonghong Wu
Keyword(s):  
Positive Solution ◽  
Differential System ◽  
Fractional Differential System ◽  
Singular Fractional Differential System ◽  
Fractional Differential

scholarly journals Positive Solutions for(n-1,1)-Type Singular Fractional Differential System with Coupled Integral Boundary Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Ying Wang ◽  
Lishan Liu ◽  
Xinguang Zhang ◽  
Yonghong Wu
Keyword(s):  
Boundary Conditions ◽  
Positive Solutions ◽  
Differential System ◽  
Integral Boundary Conditions ◽  
Integral Boundary ◽  
Fractional Differential System ◽  
Coupled Integral Boundary Conditions ◽  
Existence Of Positive Solutions ◽  
Singular Fractional Differential System ◽  
Fractional Differential

We study the positive solutions of the(n-1,1)-type fractional differential system with coupled integral boundary conditions. The conditions for the existence of positive solutions to the system are established. In addition, we derive explicit formulae for the estimation of the positive solutions and obtain the unique positive solution when certain additional conditions hold. An example is then given to demonstrate the validity of our main results.

scholarly journals Stability analysis of a nonlinear coupled implicit switched singular fractional differential system with p-Laplacian

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Manzoor Ahmad ◽  
Akbar Zada ◽  
Jehad Alzabut
Keyword(s):  
Fractional Derivative ◽  
Differential System ◽  
Fractional Derivatives ◽  
Integral Form ◽  
Uniqueness Of Solutions ◽  
Fractional Differential System ◽  
Liouville Fractional Derivative ◽  
Singular Fractional Differential System ◽  
Fractional Differential ◽  
Banach’S Contraction Principle

Abstract This paper deals with existence, uniqueness, and Hyers–Ulam stability of solutions to a nonlinear coupled implicit switched singular fractional differential system involving Laplace operator $\phi _{p}$ ϕ p . The proposed problem consists of two kinds of fractional derivatives, that is, Riemann–Liouville fractional derivative of order β and Caputo fractional derivative of order σ, where $m-1<\beta $ m − 1 < β , $\sigma < m$ σ < m , $m\in \{2,3,\dots \}$ m ∈ { 2 , 3 , … } . Prior to proceeding to the main results, the system is converted into an equivalent integral form by the help of Green’s function. Using Schauder’s fixed point theorem and Banach’s contraction principle, the existence and uniqueness of solutions are proved. The main results are demonstrated by an example.

scholarly journals On the existence of solutions for a multi-singular pointwise defined fractional system

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Ali Mansouri ◽  
Shahram Rezapour ◽  
Mehdi Shabibi
Keyword(s):  
Differential Equations ◽  
Differential System ◽  
Fractional Differential Equations ◽  
Existence Of Solutions ◽  
Natural Phenomena ◽  
Singular Equations ◽  
Fractional Differential System ◽  
Singular Fractional Differential System ◽  
Fractional Differential ◽  
Fractional System

AbstractOne of best ways for increasing our abilities in exact modeling of natural phenomena is working with a singular version of different fractional differential equations. As is well known, multi-singular equations are a modern version of singular equations. In this paper, we investigate the existence of solutions for a multi-singular fractional differential system. We consider some particular boundary value conditions on the system. By using the α-ψ-contractions and locating some control conditions, we prove that the system via infinite singular points has solutions. Finally, we provide an example to illustrate our main result.

GENERATING 3-D SCROLL GRID ATTRACTORS OF FRACTIONAL DIFFERENTIAL SYSTEMS VIA STAIR FUNCTION

2007 ◽  
Vol 17 (11) ◽  
pp. 3965-3983 ◽  
Author(s):  
WEIHUA DENG
Keyword(s):  
Differential System ◽  
Autonomous System ◽  
Function Approach ◽  
Differential Systems ◽  
Fractional Differential Systems ◽  
Fractional Differential System ◽  
Linear Autonomous System ◽  
Fractional Differential ◽  
The One ◽  
Number Of Equilibria

This paper discusses the stair function approach for the generation of scroll grid attractors of fractional differential systems. The one-directional (1-D) n-grid scroll, two-directional (2-D) (n × m)-grid scroll and three-directional (3-D) (n × m × l)-grid scroll attractors are created from a fractional linear autonomous system with a simple stair function controller. Being similar to the scroll grid attractors of classical differential systems, the scrolls of 1-D n-grid scroll, 2-D (n × m)-grid scroll and 3-D (n × m × l)-grid scroll attractors are located around the equilibria of fractional differential system on a line, on a plane or in 3D, respectively and the number of scrolls is equal to the corresponding number of equilibria.

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