scholarly journals Existence and uniqueness of positive solutions for a class of nonlinear fractional differential equations with mixed-type boundary value conditions

2018 ◽  
Vol 24 (1) ◽  
pp. 73-94 ◽  
Author(s):  
Fang Wang ◽  
Lishan Liu ◽  
Debin Kong ◽  
Yonghong Wu
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Mixed Type ◽  
Index Theory ◽  
Nonlinear Fractional Differential Equations ◽  
Fixed Point Index Theory ◽  
Fractional Differential ◽  
Type Boundary

In this article, we study a class of nonlinear fractional differential equations with mixed-type boundary conditions. The fractional derivatives are involved in the nonlinear term and the boundary conditions. By using the properties of the Green function, the fixed point index theory and the Banach contraction mapping principle based on some available operators, we obtain the existence of positive solutions and a unique positive solution of the problem. Finally, two examples are given to demonstrate the validity of our main results.

scholarly journals The Existence of Positive Solutions for Boundary Value Problem of Nonlinear Fractional Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Yanli Chen ◽  
Yongxiang Li
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Index Theory ◽  
Nonlinear Fractional Differential Equations ◽  
Fixed Point Index Theory ◽  
Existence Of Positive Solutions ◽  
Fractional Differential

We consider the existence of positive solutions for the nonlinear fractional differential equations boundary value problem-D0+αu(t)=f(t,u(t)),   0<t<1,  u(0)=u'(0)=u'(1)=0,where2<α≤3is a real number,D0+αis the Riemann-Liouville fractional derivative of orderα, andfis a given continuous function. Our analysis relies on the fixed point index theory in cones.

scholarly journals New Sequential Fractional Differential Equations with Mixed-Type Boundary Conditions

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Haiyan Zhang ◽  
Yaohong Li ◽  
Jingbao Yang
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Mixed Type ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Integral Boundary ◽  
Fractional Differential ◽  
Type Boundary ◽  
Sequential Fractional Differential Equations

In this paper, we introduce new sequential fractional differential equations with mixed-type boundary conditions CDq+kCDq−1ut=ft,ut,CDq−1ut,t∈0,1,α1u0+β1u1+γ1Iruη=ε1,η∈0,1,α2u′0+β2u′1+γ2Iru′η=ε2, where q∈1,2 is a real number, k,r>0,αi,βi,γi,εi∈ℝ,i=1,2,CDq is the Caputo fractional derivative, and the boundary conditions include antiperiodic and Riemann-Liouville fractional integral boundary value cases. Our approach to treat the above problem is based upon standard tools of fixed point theory and some new inequalities of norm form. Some existence results are obtained and well illustrated through the aid of examples.

scholarly journals Multiple Positive Solutions for a System of Nonlinear Caputo-Type Fractional Differential Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Hongyu Li ◽  
Yang Chen
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Fixed Point Index ◽  
Index Theory ◽  
Multiple Positive Solutions ◽  
Point Index ◽  
Fixed Point Index Theory ◽  
Fractional Differential

By using fixed-point index theory, we consider the existence of multiple positive solutions for a system of nonlinear Caputo-type fractional differential equations with the Riemann-Stieltjes boundary conditions.

Sign in / Sign up

Export Citation Format

Share Document