scholarly journals Nonlinear boundary value problems of fractional differential systems

2012 ◽  
Vol 64 (4) ◽  
pp. 463-475 ◽  
Author(s):  
Zhenhai Liu ◽  
Jihua Sun
Keyword(s):  
Boundary Value Problems ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Nonlinear Boundary Value Problems ◽  
Differential Systems ◽  
Fractional Differential Systems ◽  
Nonlinear Boundary Value ◽  
Fractional Differential

scholarly journals Nonlinear boundary value problems for mixed-type fractional equations and Ulam-Hyers stability

2020 ◽  
Vol 18 (1) ◽  
pp. 916-929
Author(s):  
Huiwen Wang ◽  
Fang Li
Keyword(s):  
Boundary Value Problems ◽  
Mixed Type ◽  
Fractional Derivatives ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Nonlinear Boundary Value Problems ◽  
New Techniques ◽  
Fractional Equations ◽  
Nonlinear Boundary Value ◽  
Fractional Differential

Abstract In this article, we discuss the nonlinear boundary value problems involving both left Riemann-Liouville and right Caputo-type fractional derivatives. By using some new techniques and properties of the Mittag-Leffler functions, we introduce a formula of the solutions for the aforementioned problems, which can be regarded as a novelty item. Moreover, we obtain the existence result of solutions for the aforementioned problems and present the Ulam-Hyers stability of the fractional differential equation involving two different fractional derivatives. An example is given to illustrate our theoretical result.

scholarly journals General iterative methods for nonlinear boundary value problems

1995 ◽  
Vol 37 (1) ◽  
pp. 58-85 ◽  
Author(s):  
Radha Shridharan ◽  
Ravi P. Agarwal
Keyword(s):  
Boundary Value Problems ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Nonlinear Boundary Value Problems ◽  
Constructive Theory ◽  
Differential Systems ◽  
Linear Differential Systems ◽  
Nonlinear Boundary Value ◽  
Linear Differential ◽  
Homogeneous Linear

AbstractIn this paper we shall develop existence-uniqueness as well as constructive theory for the solutions of systems of nonlinear boundary value problems when only approximations of the fundamental matrix of the associated homogeneous linear differential systems are known. To make the analysis widely applicable, all the results are proved component-wise. An illustration which dwells upon the sharpness as well as the importance of the obtained results is also presented.

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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