scholarly journals Existence and Uniqueness Results for Nonlinear Boundary Value Problems

1993 ◽  
Vol 24 (1) ◽  
pp. 77-91 ◽  
Author(s):  
D.D. Hai ◽  
K. Schmitt
Keyword(s):  
Boundary Value Problems ◽  
Existence And Uniqueness ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Nonlinear Boundary Value Problems ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Nonlinear Boundary Value

scholarly journals Existence and Iterative Method for Some Riemann Fractional Nonlinear Boundary Value Problems

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 961 ◽  
Author(s):  
Imed Bachar ◽  
Habib Mâagli ◽  
Hassan Eltayeb
Keyword(s):  
Iterative Method ◽  
Boundary Value Problems ◽  
Fourth Order ◽  
Existence And Uniqueness ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Uniqueness Of Solution ◽  
Nonlinear Boundary Value Problems ◽  
Nonlinear Boundary Value ◽  
Appl Math

In this paper, we prove the existence and uniqueness of solution for some Riemann–Liouville fractional nonlinear boundary value problems. The positivity of the solution and the monotony of iterations are also considered. Some examples are presented to illustrate the main results. Our results generalize those obtained by Wei et al (Existence and iterative method for some fourth order nonlinear boundary value problems. Appl. Math. Lett. 2019, 87, 101–107.) to the fractional setting.

scholarly journals Existence and uniqueness of solutions for a class of fractional nonlinear boundary value problems under mild assumptions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Imed Bachar ◽  
Habib Mâagli ◽  
Hassan Eltayeb
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Existence And Uniqueness ◽  
Nonlinear Boundary ◽  
Continuous Solution ◽  
Boundary Value ◽  
Nonlinear Boundary Value Problems ◽  
Uniqueness Of Solutions ◽  
Nonlinear Boundary Value ◽  
Appl Math

AbstractWe deal with the following Riemann–Liouville fractional nonlinear boundary value problem: $$ \textstyle\begin{cases} \mathcal{D}^{\alpha }v(x)+f(x,v(x))=0, & 2< \alpha \leq 3, x\in (0,1), \\ v(0)=v^{\prime }(0)=v(1)=0. \end{cases} $$ { D α v ( x ) + f ( x , v ( x ) ) = 0 , 2 < α ≤ 3 , x ∈ ( 0 , 1 ) , v ( 0 ) = v ′ ( 0 ) = v ( 1 ) = 0 . Under mild assumptions, we prove the existence of a unique continuous solution v to this problem satisfying $$ \bigl\vert v(x) \bigr\vert \leq cx^{\alpha -1}(1-x)\quad\text{for all }x \in [ 0,1]\text{ and some }c>0. $$ | v ( x ) | ≤ c x α − 1 ( 1 − x ) for all  x ∈ [ 0 , 1 ]  and some  c > 0 . Our results improve those obtained by Zou and He (Appl. Math. Lett. 74:68–73, 2017).

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