scholarly journals Positive Solutions of an Initial Value Problem for Nonlinear Fractional Differential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-7 ◽  
Author(s):  
D. Baleanu ◽  
H. Mohammadi ◽  
Sh. Rezapour
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Positive Solutions ◽  
Initial Value Problem ◽  
Initial Value ◽  
Nonlinear Fractional Differential Equation ◽  
Multiplicity Results ◽  
Existence And Multiplicity ◽  
Fractional Differential ◽  
Multiplicity Of Positive Solutions

We investigate the existence and multiplicity of positive solutions for the nonlinear fractional differential equation initial value problemD0+αu(t)+D0+βu(t)=f(t,u(t)), u(0)=0, 0<t<1, where0<β<α<1, D0+αis the standard Riemann-Liouville differentiation andf:[0,1]×[0,∞)→[0,∞)is continuous. By using some fixed-point results on cones, some existence and multiplicity results of positive solutions are obtained.

scholarly journals Existence of Concave Positive Solutions for Boundary Value Problem of Nonlinear Fractional Differential Equation withp-Laplacian Operator

2010 ◽  
Vol 2010 ◽  
pp. 1-17 ◽  
Author(s):  
Jinhua Wang ◽  
Hongjun Xiang ◽  
ZhiGang Liu
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Boundary Value Problem ◽  
Fractional Differential Equation ◽  
Positive Solutions ◽  
Boundary Value ◽  
Laplacian Operator ◽  
Nonlinear Fractional Differential Equation ◽  
Existence And Multiplicity ◽  
Fractional Differential

We consider the existence and multiplicity of concave positive solutions for boundary value problem of nonlinear fractional differential equation withp-Laplacian operatorD0+γ(ϕp(D0+αu(t)))+f(t,u(t),D0+ρu(t))=0,0<t<1,u(0)=u′(1)=0,u′′(0)=0,D0+αu(t)|t=0=0, where0<γ<1,2<α<3,0<ρ⩽1,D0+αdenotes the Caputo derivative, andf:[0,1]×[0,+∞)×R→[0,+∞)is continuous function,ϕp(s)=|s|p-2s,p>1,  (ϕp)-1=ϕq,  1/p+1/q=1. By using fixed point theorem, the results for existence and multiplicity of concave positive solutions to the above boundary value problem are obtained. Finally, an example is given to show the effectiveness of our works.

scholarly journals Positive Solutions of a Fractional Boundary Value Problem with Changing Sign Nonlinearity

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Yongqing Wang ◽  
Lishan Liu ◽  
Yonghong Wu
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Boundary Value ◽  
Fractional Boundary Value Problem ◽  
Nonlinear Fractional Differential Equation ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Existence Of Positive Solutions ◽  
Fractional Differential

We discuss the existence of positive solutions of a boundary value problem of nonlinear fractional differential equation with changing sign nonlinearity. We first derive some properties of the associated Green function and then obtain some results on the existence of positive solutions by means of the Krasnoselskii's fixed point theorem in a cone.

Existence of positive solutions for systems of nonlinear fractional differential equation with p-Laplacian

2019 ◽  
Vol 13 (05) ◽  
pp. 2050089 ◽  
Author(s):  
S. Nageswara Rao ◽  
Meshari Alesemi
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problems ◽  
Fractional Differential Equation ◽  
Positive Solutions ◽  
Sufficient Conditions ◽  
Nonlinear Fractional Differential Equation ◽  
Existence Of Positive Solutions ◽  
Fractional Differential

In this paper, we establish sufficient conditions for the existence of positive solutions for a system of nonlinear fractional [Formula: see text]-Laplacian boundary value problems under different combinations of superlinearity and sublinearity of the nonlinearities via the Guo–Krasnosel’skii fixed point theorem. Moreover, an example is given to illustrate our results.

scholarly journals Positive Solutions of Nonlinear Fractional Differential Equations with Integral Boundary Value Conditions

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
J. Caballero ◽  
I. Cabrera ◽  
K. Sadarangani
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Positive Solutions ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Partially Ordered Sets ◽  
Ordered Sets ◽  
Nonlinear Fractional Differential Equation ◽  
Integral Boundary ◽  
Fractional Differential

We investigate the existence and uniqueness of positive solutions of the following nonlinear fractional differential equation with integral boundary value conditions, , , where , and is the Caputo fractional derivative and is a continuous function. Our analysis relies on a fixed point theorem in partially ordered sets. Moreover, we compare our results with others that appear in the literature.

scholarly journals Existence and Uniqueness of Solutions for Initial Value Problem of Nonlinear Fractional Differential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-14
Author(s):  
Qiuping Li ◽  
Shurong Sun ◽  
Ping Zhao ◽  
Zhenlai Han
Keyword(s):  
Differential Equation ◽  
Initial Value Problem ◽  
Existence And Uniqueness ◽  
Upper And Lower Solutions ◽  
Initial Value ◽  
Uniqueness Of Solutions ◽  
Nonlinear Fractional Differential Equation ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Fractional Differential

We discuss the initial value problem for the nonlinear fractional differential equationL(D)u=f(t,u),  t∈(0,1],  u(0)=0, whereL(D)=Dsn-an-1Dsn-1-⋯-a1Ds1,0<s1<s2<⋯<sn<1, andaj<0,j=1,2,…,n-1,Dsjis the standard Riemann-Liouville fractional derivative andf:[0,1]×ℝ→ℝis a given continuous function. We extend the basic theory of differential equation, the method of upper and lower solutions, and monotone iterative technique to the initial value problem. Some existence and uniqueness results are established.

scholarly journals Positive Solutions for Boundary Value Problem of Nonlinear Fractional Differential Equation

2007 ◽  
Vol 2007 ◽  
pp. 1-8 ◽  
Author(s):  
Moustafa El-Shahed
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Boundary Value ◽  
Fractional Boundary Value Problem ◽  
Nonlinear Fractional Differential Equation ◽  
Existence And Nonexistence ◽  
Liouville Fractional Derivative ◽  
Fractional Differential

We are concerned with the existence and nonexistence of positive solutions for the nonlinear fractional boundary value problem:D0+αu(t)+λa(t) f(u(t))=0, 0<t<1, u(0)=u′(0)=u′(1)=0,where2<α<3is a real number andD0+αis the standard Riemann-Liouville fractional derivative. Our analysis relies on Krasnoselskiis fixed point theorem of cone preserving operators. An example is also given to illustrate the main results.

Multiplicity Results for Integral Boundary Value Problems of Fractional Order with Parametric Dependence

2015 ◽  
Vol 18 (1) ◽  
Author(s):  
Alberto Cabada ◽  
Zakaria Hamdi
Keyword(s):  
Differential Equation ◽  
Fractional Differential Equation ◽  
Boundary Value ◽  
Nonlinear Fractional Differential Equation ◽  
Integral Boundary ◽  
Multiplicity Results ◽  
Parametric Dependence ◽  
Existence And Multiplicity ◽  
Fractional Differential ◽  
Integral Boundary Value Problems

AbstractThis paper is devoted to the study of nonlinear fractional differential equation with parameter dependence and integral boundary value conditions. In the paper various existence and multiplicity results for positive solutions are derived depending of different values of the parameter. Some illustrative examples are also discussed.

scholarly journals System of fractional boundary value problem with p-Laplacian and advanced arguments

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Amina Mahdjouba ◽  
Juan J. Nieto ◽  
Abdelghani Ouahab
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Positive Solutions ◽  
Point Theorem ◽  
Existence Result ◽  
Fractional Boundary Value Problem ◽  
Existence And Multiplicity ◽  
Fractional Differential ◽  
Multiplicity Of Positive Solutions

AbstractIn this paper, we discuss the existence and multiplicity of positive solutions for a system of fractional differential equations with boundary condition and advanced arguments. The existence result is proved via Leray–Schauder’s fixed point theorem type in a vector Banach space. Further, by using a new fixed point theorem in order Banach space, we study the multiplicity of positive solutions. Finally, some examples are given to illustrate our results.

FEATURES OF SEEPAGE OF A LIQUID TO A CHINK IN THE CRACKED DEFORMABLE LAYER

2010 ◽  
Vol 01 (03) ◽  
pp. 333-347 ◽  
Author(s):  
T. S. ALEROEV ◽  
H. T. ALEROEVA ◽  
JIANFEI HUANG ◽  
NINGMING NIE ◽  
YIFA TANG ◽  
...  
Keyword(s):  
Differential Equation ◽  
Initial Value Problem ◽  
Numerical Scheme ◽  
Variable Coefficients ◽  
Initial Value ◽  
Nonlinear Fractional Differential Equation ◽  
Fractional Model ◽  
New Model ◽  
Whole Process ◽  
Fractional Differential

We establish a new model for seepage of a liquid to a chink in the cracked deformable layer, an initial value problem of nonlinear fractional differential equation with variable coefficients, then design a numerical scheme of order 2 to solve this initial value problem. This new model theoretically explains the operating thickness H of a layer depending on the values of pressure gradient on the whole chink rather than on one point, which is practiced by a large amount of data. Compared with the Dontsov equation, our fractional model considers more aspects of the whole process. The earlier rejected results can also be considered in the display lines of the fractional model.

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