scholarly journals A generalized Lyapunov inequality for a higher-order fractional boundary value problem

2016 ◽  
Vol 2016 (1) ◽  
Author(s):  
Dexiang Ma
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Higher Order ◽  
Fractional Boundary Value Problem ◽  
Lyapunov Inequality

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 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.

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