scholarly journals Existence and Extremal Solution of Boundary Value Problem for Nonlinear Hybrid Fractional Differential Equation in Banach Algebras

2020 ◽  
Vol 1 ◽  
pp. 23-32
Author(s):  
B.D. Karande ◽  
Pravin M. More
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Boundary Value Problem ◽  
Fractional Differential Equation ◽  
Boundary Value ◽  
Banach Algebras ◽  
Extremal Solution ◽  
Hybrid Fixed Point Theorem ◽  
Fractional Differential ◽  
Nonlinear Hybrid

In this work we study the existence and extremal solution for the boundary value problem of the nonlinear hybrid fractional differential equation by using hybrid fixed point theorem in Banach Algebra due to Dhage’s theorem.

Tripled fixed point theorems and applications to a fractional differential equation boundary value problem

2017 ◽  
Vol 10 (03) ◽  
pp. 1750056 ◽  
Author(s):  
Hojjat Afshari ◽  
Alireza Kheiryan
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Boundary Value Problem ◽  
Fractional Differential Equation ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Tripled Fixed Point ◽  
Equation Boundary ◽  
Fractional Differential

In this article we study a class of mixed monotone operators with convexity on ordered Banach spaces and present some new tripled fixed point theorems by means of partial order theory, we get the existence and uniqueness of tripled fixed points without assuming the operator to be compact or continuous, which extend the existing corresponding results. As applications, we utilize the results obtained in this paper to study the existence and uniqueness of positive solutions for a fractional differential equation boundary value problem.

scholarly journals Positive Solutions for a Coupled System of Nonlinear Semipositone Fractional Boundary Value Problems

2019 ◽  
Vol 2019 ◽  
pp. 1-9 ◽  
Author(s):  
S. Nageswara Rao ◽  
M. Zico Meetei
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Positive Solution ◽  
Fractional Differential Equation ◽  
Boundary Value ◽  
Coupled System ◽  
Fractional Differential ◽  
Fractional Boundary Value Problems

In this paper, we consider a four-point coupled boundary value problem for system of the nonlinear semipositone fractional differential equation D0+αu(t)+λf(t,u(t),v(t))=0,  0<t<1, D0+αv(t)+μg(t,u(t),v(t))=0,  0<t<1, u(0)=v(0)=0,  a1D0+βu(1)=b1D0+βv(ξ), a2D0+βv(1)=b2D0+βu(η),  η,ξ∈(0,1), where the coefficients ai,bi,i=1,2 are real positive constants, α∈(1,2],β∈(0,1],D0+α, D0+β are the standard Riemann-Liouville derivatives. Values of the parameters λ and μ are determined for which boundary value problem has positive solution by utilizing a fixed point theorem on cone.

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 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 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.

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