scholarly journals A sufficient condition for the existence of a positive solution for a nonlinear fractional differential equation with the Riemann–Liouville derivative

2012 ◽  
Vol 25 (11) ◽  
pp. 1986-1992 ◽  
Author(s):  
Yang Liu ◽  
weiguo Zhang ◽  
Xiping Liu
Keyword(s):  
Differential Equation ◽  
Positive Solution ◽  
Fractional Differential Equation ◽  
Sufficient Condition ◽  
Nonlinear Fractional Differential Equation ◽  
Liouville Derivative ◽  
Fractional Differential

scholarly journals Existence of Positive Solution for BVP of Nonlinear Fractional Differential Equation

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
Jun-Rui Yue ◽  
Jian-Ping Sun ◽  
Shuqin Zhang
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Fractional Derivative ◽  
Positive Solution ◽  
Fractional Differential Equation ◽  
Nonlinear Fractional Differential Equation ◽  
Krasnoselskii Fixed Point Theorem ◽  
Fractional Differential

We consider the following boundary value problem of nonlinear fractional differential equation:(CD0+αu)(t)=f(t,u(t)),  t∈[0,1],  u(0)=0,   u′(0)+u′′(0)=0,  u′(1)+u′′(1)=0, whereα∈(2,3]is a real number, CD0+αdenotes the standard Caputo fractional derivative, andf:[0,1]×[0,+∞)→[0,+∞)is continuous. By using the well-known Guo-Krasnoselskii fixed point theorem, we obtain the existence of at least one positive solution for the above 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 Solution for the Nonlinear Hadamard Type Fractional Differential Equation withp-Laplacian

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Ya-ling Li ◽  
Shi-you Lin
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Continuous Function ◽  
Fractional Derivative ◽  
Positive Solution ◽  
Fractional Differential Equation ◽  
Fixed Point Theorems ◽  
Laplacian Operator ◽  
Nonlinear Fractional Differential Equation ◽  
Fractional Differential

We study the following nonlinear fractional differential equation involving thep-Laplacian operatorDβφpDαut=ft,ut,1<t<e,u1=u′1=u′e=0,Dαu1=Dαue=0, where the continuous functionf:1,e×0,+∞→[0,+∞),2<α≤3,1<β≤2.Dαdenotes the standard Hadamard fractional derivative of the orderα, the constantp>1, and thep-Laplacian operatorφps=sp-2s. We show some results about the existence and the uniqueness of the positive solution by using fixed point theorems and the properties of Green's function and thep-Laplacian operator.

scholarly journals Oscillation criteria for nonlinear fractional differential equation with damping term

Open Physics ◽  
2016 ◽  
Vol 14 (1) ◽  
pp. 119-128 ◽  
Author(s):  
Mustafa Bayram ◽  
Hakan Adiguzel ◽  
Aydin Secer
Keyword(s):  
Differential Equation ◽  
Fractional Differential Equation ◽  
Riccati Transformation ◽  
Damping Term ◽  
Nonlinear Fractional Differential Equation ◽  
Oscillation Criteria ◽  
Generalized Riccati Transformation ◽  
Liouville Derivative ◽  
Fractional Differential ◽  
Oscillation Of Solutions

AbstractIn this paper, we study the oscillation of solutions to a non-linear fractional differential equation with damping term. The fractional derivative is defined in the sense of the modified Riemann-Liouville derivative. By using a variable transformation, a generalized Riccati transformation, inequalities, and integration average techniquewe establish new oscillation criteria for the fractional differential equation. Several illustrative examples are also given.

scholarly journals On establishing qualitative theory to nonlinear boundary value problem of fractional differential equations

2021 ◽  
Author(s):  
Amjad Ali ◽  
Nabeela Khan ◽  
Seema Israr
Keyword(s):  
Differential Equation ◽  
Positive Solution ◽  
Fractional Differential Equation ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Alternative Form ◽  
Nonlinear Fractional Differential Equation ◽  
Main Work ◽  
Greens Function ◽  
Fractional Differential

AbstractIn this article, we study a class of nonlinear fractional differential equation for the existence and uniqueness of a positive solution and the Hyers–Ulam-type stability. To proceed this work, we utilize the tools of fixed point theory and nonlinear analysis to investigate the concern theory. We convert fractional differential equation into an integral alternative form with the help of the Greens function. Using the desired function, we studied the existence of a positive solution and uniqueness for proposed class of fractional differential equation. In next section of this work, the author presents stability analysis for considered problem and developed the conditions for Ulam’s type stabilities. Furthermore, we also provided two examples to illustrate our main work.

scholarly journals Positive solution for nonlinear fractional differential equation with nonlocal multi-point condition

2020 ◽  
Vol 21 (2) ◽  
pp. 427-440 ◽  
Author(s):  
Piyachat Borisut ◽  
◽  
Poom Kumam ◽  
Idris Ahmed ◽  
Kanokwan Sitthithakerngkiet ◽  
...  
Keyword(s):  
Differential Equation ◽  
Positive Solution ◽  
Fractional Differential Equation ◽  
Nonlinear Fractional Differential Equation ◽  
Point Condition ◽  
Fractional Differential
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