scholarly journals Three-point boundary value problems of fractional functional differential equations with delay

2013 ◽  
Vol 2013 (1) ◽  
pp. 38 ◽  
Author(s):  
Yanan Li ◽  
Shurong Sun ◽  
Dianwu Yang ◽  
Zhenlai Han
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Functional Differential Equations ◽  
Point Boundary ◽  
Functional Differential ◽  
Fractional Functional Differential Equations ◽  
Equations With Delay ◽  
Fractional Functional

scholarly journals On Nonseparated Three-Point Boundary Value Problems for Linear Functional Differential Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-22 ◽  
Author(s):  
A. Rontó ◽  
M. Rontó
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Linear Functional ◽  
Boundary Value ◽  
Functional Differential Equations ◽  
Special Kind ◽  
Successive Approximations ◽  
Point Problem ◽  
Point Boundary ◽  
Functional Differential

For a system of linear functional differential equations, we consider a three-point problem with nonseparated boundary conditions determined by singular matrices. We show that, to investigate such a problem, it is often useful to reduce it to a parametric family of two-point boundary value problems for a suitably perturbed differential system. The auxiliary parametrised two-point problems are then studied by a method based upon a special kind of successive approximations constructed explicitly, whereas the values of the parameters that correspond to solutions of the original problem are found from certain numerical determining equations. We prove the uniform convergence of the approximations and establish some properties of the limit and determining functions.

scholarly journals Numerical Studies for Fractional Functional Differential Equations with Delay Based on BDF-Type Shifted Chebyshev Approximations

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
V. G. Pimenov ◽  
A. S. Hendy
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
True Solution ◽  
New Approach ◽  
Numerical Studies ◽  
Runge Kutta Method ◽  
Functional Differential ◽  
Fractional Functional Differential Equations ◽  
Equations With Delay ◽  
Fractional Functional

Fractional functional differential equations with delay (FDDEs) have recently played a significant role in modeling of many real areas of sciences such as physics, engineering, biology, medicine, and economics. FDDEs often cannot be solved analytically so the approximate and numerical methods should be adapted to solve these types of equations. In this paper we consider a new method of backward differentiation formula- (BDF-) type for solving FDDEs. This approach is based on the interval approximation of the true solution using the Clenshaw and Curtis formula that is based on the truncated shifted Chebyshev polynomials. It is shown that the new approach can be reformulated in an equivalent way as a Runge-Kutta method and the Butcher tableau of this method is given. Estimation of local and global truncating errors is deduced and this leads to the proof of the convergence for the proposed method. Illustrative examples of FDDEs are included to demonstrate the validity and applicability of the proposed approach.

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