Homoclinic solutions for Hamiltonian systems with variable-order fractional derivatives

2019 ◽  
Vol 65 (8) ◽  
pp. 1412-1432
Author(s):  
Mingqi Xiang ◽  
Di Yang ◽  
Binlin Zhang
Keyword(s):  
Hamiltonian Systems ◽  
Fractional Derivatives ◽  
Homoclinic Solutions ◽  
Variable Order ◽  
Variable Order Fractional Derivatives

scholarly journals Explicit Finite-Difference Scheme for the Numerical Solution of the Model Equation of Nonlinear Hereditary Oscillator with Variable-Order Fractional Derivatives

2016 ◽  
Vol 26 (3) ◽  
pp. 429-435 ◽  
Author(s):  
Roman I. Parovik
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Fractional Derivatives ◽  
Stability And Convergence ◽  
Variable Order ◽  
The Difference ◽  
Explicit Finite Difference ◽  
The Stability ◽  
Variable Order Fractional Derivatives

Abstract The paper deals with the model of variable-order nonlinear hereditary oscillator based on a numerical finite-difference scheme. Numerical experiments have been carried out to evaluate the stability and convergence of the difference scheme. It is argued that the approximation, stability and convergence are of the first order, while the scheme is stable and converges to the exact solution.

A computational approach for the solution of a class of variable-order fractional integro-differential equations with weakly singular kernels

2017 ◽  
Vol 20 (4) ◽  
Author(s):  
Behrouz Parsa Moghaddam ◽  
José António Tenreiro Machado
Keyword(s):  
Differential Equation ◽  
Numerical Scheme ◽  
Fractional Derivatives ◽  
Spline Interpolation ◽  
Computational Approach ◽  
Variable Order ◽  
Weakly Singular Kernels ◽  
Weakly Singular ◽  
Singular Kernels ◽  
Variable Order Fractional Derivatives

AbstractA new computational approach for approximating of variable-order fractional derivatives is proposed. The technique is based on piecewise cubic spline interpolation. The method is extended to a class of nonlinear variable-order fractional integro-differential equation with weakly singular kernels. Illustrative examples are discussed, demonstrating the performance of the numerical scheme.

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