scholarly journals Existence of a Positive Solution for a Singular Fractional Boundary Value Problem with Fractional Boundary Conditions using Convolution and Lower Order Problems

2021 ◽  
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Positive Solution ◽  
Lower Order ◽  
Boundary Value ◽  
Fractional Boundary Value Problem ◽  
Fractional Boundary Conditions

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.

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.

Lyapunov-type inequality for an anti-periodic fractional boundary value problem

2017 ◽  
Vol 20 (1) ◽  
Author(s):  
Rui A. C. Ferreira
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Type Inequality ◽  
Periodic Boundary Conditions ◽  
Fractional Boundary Value Problem ◽  
Research Directions ◽  
Lyapunov Type Inequality

AbstractIn this note we present a Lyapunov-type inequality for a fractional boundary value problem with anti-periodic boundary conditions, that we show to be a generalization of a classical one. Moreover, we address the issue of further research directions for such type of inequalities.

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 A New Proof for Lyapunov-Type Inequality on the Fractional Boundary Value Problem

Symmetry ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 29
Author(s):  
Yumei Zou ◽  
Xin Zhang ◽  
Hongyu Li
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Green’S Function ◽  
Boundary Value Problems ◽  
Green's Function ◽  
Boundary Value ◽  
Type Inequality ◽  
Fractional Boundary Value Problem ◽  
Lyapunov Type Inequality ◽  
Fractional Boundary Value Problems

In this article, some new Lyapunov-type inequalities for a class of fractional boundary value problems are established by use of the nonsymmetry property of Green’s function corresponding to appropriate boundary conditions.

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