scholarly journals PROPERTIES AND UNIQUE POSITIVE SOLUTION FOR FRACTIONAL BOUNDARY VALUE PROBLEM WITH TWO PARAMETERS ON THE HALF-LINE

2020 ◽  
Vol 0 (0) ◽  
pp. 0-0
Author(s):  
Wenxia Wang ◽  
◽  
Xilan Liu ◽  
Keyword(s):  
Boundary Value Problem ◽  
Positive Solution ◽  
Boundary Value ◽  
Half Line ◽  
Fractional Boundary Value Problem ◽  
Unique Positive Solution ◽  
Two Parameters

Unique positive solution for a fractional boundary value problem

2013 ◽  
Vol 16 (4) ◽  
Author(s):  
Keyu Zhang ◽  
Jiafa Xu
Keyword(s):  
Boundary Value Problem ◽  
Positive Solution ◽  
Boundary Value ◽  
Upper And Lower Solutions ◽  
Monotone Iterative Technique ◽  
Iterative Technique ◽  
Fractional Boundary Value Problem ◽  
Unique Positive Solution ◽  
Monotone Iterative ◽  
Liouville Fractional Derivative

AbstractIn this work we consider the unique positive solution for the following fractional boundary value problem $\left\{ \begin{gathered} D_{0 + }^\alpha u(t) = - f(t,u(t)),t \in [0,1], \hfill \\ u(0) = u'(0) = u'(1) = 0. \hfill \\ \end{gathered} \right. $ Here α ∈ (2, 3] is a real number, D 0+α is the standard Riemann-Liouville fractional derivative of order α. By using the method of upper and lower solutions and monotone iterative technique, we also obtain that there exists a sequence of iterations uniformly converges to the unique solution.

scholarly journals Existence of a unique positive solution for a singular fractional boundary value problem

2018 ◽  
Vol 34 (1) ◽  
pp. 57-64
Author(s):  
E. T. KARIMOV ◽  
◽  
K. SADARANGANI ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Positive Solution ◽  
Fractional Order ◽  
Boundary Value ◽  
Order Equation ◽  
Fractional Boundary Value Problem ◽  
Unique Positive Solution

In the present work, we discuss the existence of a unique positive solution of a boundary value problem for a nonlinear fractional order equation with singularity. Precisely, order of equation Dα 0+u(t) = f(t, u(t)) belongs to (3, 4] and f has a singularity at t = 0 and as a boundary conditions we use... Using a fixed point theorem, we prove the existence of unique positive solution of the considered problem.

Uniqueness of Positive Solutions for a Fractional Boundary Value Problem

2014 ◽  
Vol 644-650 ◽  
pp. 2038-2041
Author(s):  
Yi Jiang ◽  
Yan Xu Hong
Keyword(s):  
Boundary Value Problem ◽  
Fractional Derivative ◽  
Real Number ◽  
Positive Solution ◽  
Arbitrary Function ◽  
Boundary Value ◽  
Iterative Sequence ◽  
Fractional Boundary Value Problem ◽  
Unique Positive Solution ◽  
Fractional Differential

In this paper, we investigate the boundary value problem of the nonlinear fractional differential equationwhere is a real number, is the Riemann-Liouville's fractional derivative, and is continuous. we obtain that the unique positive solution can be uniformly approximated by any iterative sequence, initiated by an arbitrary function that is nonnegative and continuous, and does not identically vanish on [0,1].

scholarly journals Existence and Exact Asymptotic Behavior of Positive Solutions for a Fractional Boundary Value Problem

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Habib Mâagli ◽  
Noureddine Mhadhebi ◽  
Noureddine Zeddini
Keyword(s):  
Asymptotic Behavior ◽  
Continuous Function ◽  
Boundary Value Problem ◽  
Positive Solution ◽  
Positive Solutions ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Fractional Boundary Value Problem ◽  
Exact Asymptotic Behavior ◽  
Nonnegative Continuous Function

We establish the existence and uniqueness of a positive solution for the fractional boundary value problem , with the condition , where , and is a nonnegative continuous function on that may be singular at or .

scholarly journals Existence Result and Uniqueness for Some Fractional Problem

Mathematics ◽  
2019 ◽  
Vol 7 (6) ◽  
pp. 516 ◽  
Author(s):  
Guotao Wang ◽  
Abdeljabbar Ghanmi ◽  
Samah Horrigue ◽  
Samar Madian
Keyword(s):  
Boundary Value Problem ◽  
Positive Solution ◽  
Existence Result ◽  
Boundary Value ◽  
Lower And Upper Solutions ◽  
Fractional Boundary Value Problem

In this article, by the use of the lower and upper solutions method, we prove the existence of a positive solution for a Riemann–Liouville fractional boundary value problem. Furthermore, the uniqueness of the positive solution is given. To demonstrate the serviceability of the main results, some examples are presented.

scholarly journals Positive solution for singular third-order BVPs on the half line with first-order derivative dependence

2021 ◽  
Vol 13 (1) ◽  
pp. 105-126
Author(s):  
Abdelhamid Benmezaï ◽  
El-Djouher Sedkaoui
Keyword(s):  
Boundary Value Problem ◽  
Positive Solution ◽  
Positive Constant ◽  
Space Variable ◽  
Boundary Value ◽  
Order Derivative ◽  
Half Line ◽  
Third Order ◽  
First Order ◽  
The Third

Abstract In this paper, we investigate the existence of a positive solution to the third-order boundary value problem { - u ‴ ( t ) + k 2 u ′ ( t ) = φ ( t ) f ( t , u ( t ) , u ′ ( t ) ) ,       t > 0 u ( 0 ) = u ′ ( 0 ) = u ′ ( + ∞ ) = 0 , \left\{ \matrix{- u'''\left( t \right) + {k^2}u'\left( t \right) = \phi \left( t \right)f\left( {t,u\left( t \right),u'\left( t \right)} \right),\,\,\,t > 0 \hfill \cr u\left( 0 \right) = u'\left( 0 \right) = u'\left( { + \infty } \right) = 0, \hfill \cr} \right. where k is a positive constant, ϕ ∈ L1 (0;+ ∞) is nonnegative and does vanish identically on (0;+ ∞) and the function f : ℝ+ × (0;+ ∞) × (0;+ ∞) → ℝ+ is continuous and may be singular at the space variable and at its derivative.

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