scholarly journals Hartman–Wintner type inequalities for a class of fractional BVPs with higher order

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Jackie Harjani ◽  
Kishin Sadarangani ◽  
Bessem Samet
Keyword(s):  
Lower Bound ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Higher Order ◽  
Fractional Operator ◽  
Fractional Boundary Value Problem

Abstract In this paper, we derive some Hartman–Wintner type inequalities for a certain higher order fractional boundary value problem. As an application of our results, we obtain a lower bound for the eigenvalues of the corresponding fractional operator.

Positive solutions for a semipositone fractional boundary value problem with a forcing term

2012 ◽  
Vol 15 (1) ◽  
Author(s):  
John Graef ◽  
Lingju Kong ◽  
Bo Yang
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Higher Order ◽  
Fractional Boundary Value Problem ◽  
Forcing Term

AbstractThe authors obtain sufficient conditions for the existence of at least one and two positive solutions of a higher order semipositone fractional boundary value problem with a forcing term in the differential equation. Examples are included to illustrate the results.

scholarly journals Nontrivial Solutions for a Higher Order Nonlinear Fractional Boundary Value Problem Involving Riemann-Liouville Fractional Derivatives

2019 ◽  
Vol 2019 ◽  
pp. 1-11 ◽  
Author(s):  
Keyu Zhang ◽  
Donal O’Regan ◽  
Jiafa Xu ◽  
Zhengqing Fu
Keyword(s):  
Boundary Value Problem ◽  
Topological Degree ◽  
Fractional Derivatives ◽  
Boundary Value ◽  
Higher Order ◽  
Fractional Boundary Value Problem ◽  
Nontrivial Solutions ◽  
Derivatives Of

In this paper using topological degree we study the existence of nontrivial solutions for a higher order nonlinear fractional boundary value problem involving Riemann-Liouville fractional derivatives. Here, the nonlinearity can be sign-changing and can also depend on the derivatives of unknown functions.

scholarly journals Monotone and Concave Positive Solutions to a Boundary Value Problem for Higher-Order Fractional Differential Equation

2011 ◽  
Vol 2011 ◽  
pp. 1-14 ◽  
Author(s):  
Jinhua Wang ◽  
Hongjun Xiang ◽  
Yuling Zhao
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Fractional Differential Equation ◽  
Boundary Value ◽  
Higher Order ◽  
Fractional Boundary Value Problem ◽  
Interesting Point ◽  
Nonlinear Fractional Differential Equation ◽  
Existence And Multiplicity ◽  
Fractional Differential

We consider boundary value problem for nonlinear fractional differential equationD0+αu(t)+f(t,u(t))=0,  0<t<1,  n-1<α≤n,  n>3,  u(0)=u'(1)=u′′(0)=⋯=u(n-1)(0)=0, whereD0+αdenotes the Caputo fractional derivative. By using fixed point theorem, we obtain some new results for the existence and multiplicity of solutions to a higher-order fractional boundary value problem. The interesting point lies in the fact that the solutions here are positive, monotone, and concave.

Existence of solutions for a higher order fractional boundary value problem posed on the half-line

2019 ◽  
Vol 12 (01) ◽  
pp. 1950008
Author(s):  
A. Boucenna ◽  
T. Moussaoui
Keyword(s):  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Monotone Operators ◽  
Higher Order ◽  
Half Line ◽  
Fractional Boundary Value Problem ◽  
Uniqueness Of Solutions ◽  
Continuous Embedding

The aim of this paper is to study the existence and uniqueness of solutions for a boundary value problem associated with a fractional nonlinear differential equation with higher order posed on the half-line. An appropriate continuous embedding for suitable Banach spaces are proved and the Minty–Browder theorem for monotone operators is used in the proof of existence of solutions for a boundary value problem of fractional order posed on the half-line.

scholarly journals Existence of Positive Solutions for a Kind of Fractional Boundary Value Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Hongjie Liu ◽  
Xiao Fu ◽  
Liangping Qi
Keyword(s):  
Fixed Point ◽  
Green Function ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Boundary Value ◽  
Fractional Boundary Value Problem ◽  
Existence Of Positive Solutions ◽  
Liouville Fractional Derivative ◽  
Fractional Boundary Value Problems

We are concerned with the following nonlinear three-point fractional boundary value problem:D0+αut+λatft,ut=0,0<t<1,u0=0, andu1=βuη, where1<α≤2,0<β<1,0<η<1,D0+αis the standard Riemann-Liouville fractional derivative,at>0is continuous for0≤t≤1, andf≥0is continuous on0,1×0,∞. By using Krasnoesel'skii's fixed-point theorem and the corresponding Green function, we obtain some results for the existence of positive solutions. At the end of this paper, we give an example to illustrate our main results.

Fuzzy fractional boundary value problem

2021 ◽  
Author(s):  
Elhoussain ARHRRABI ◽  
Abdellah TAQBIBT ◽  
M'hamed ELOMARI ◽  
Said MELLIANI ◽  
Lalla saadia CHADLI
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Fractional Boundary Value Problem
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