scholarly journals Generalized monotone iterative method for nonlinear boundary value problems with causal operators

2014 ◽  
Vol 2014 (1) ◽  
Author(s):  
Wen-Li Wang ◽  
Jing-Feng Tian
Keyword(s):  
Iterative Method ◽  
Boundary Value Problems ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Monotone Iterative Method ◽  
Nonlinear Boundary Value Problems ◽  
Monotone Iterative ◽  
Nonlinear Boundary Value ◽  
Causal Operators

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 Monotone Iterative Solutions for Nonlinear Boundary Value Problems of Fractional Differential Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Chaozhu Hu ◽  
Bin Liu ◽  
Songfa Xie
Keyword(s):  
Boundary Value Problems ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Nonlinear Boundary Value Problems ◽  
New Approach ◽  
Monotone Iterative ◽  
Actual Solution ◽  
Nonlinear Boundary Value ◽  
Iterative Solutions ◽  
Fractional Differential

By means of the method of quasi-lower and quasi-upper solutions and monotone iterative technique, we consider the nonlinear boundary value problems with Caputo fractional derivative and introduce two well-defined monotone sequences of quasi-lower and quasi-upper solutions which converge uniformly to the actual solution of the problem, and then the existence results of the solution for the problems are established. A numerical iterative scheme is introduced to obtain an accurate approximate solution and to give one example to demonstrate the accuracy and efficiency of the new approach.

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