The numerical solution of linear multi-term fractional differential equations: systems of equations
Journal of Computational and Applied Mathematics
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IEEE Transactions on Information Theory
Numerical algorithm for the time fractional Fokker-Planck equation
Journal of Computational Physics
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Journal of Computational and Applied Mathematics
Fractional-order chaotic systems
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Journal of Computational and Applied Mathematics
Random-order fractional differential equation models
Signal Processing
Modeling and numerical analysis of fractional-order Bloch equations
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Journal of Computational Physics
Computers & Mathematics with Applications
Novel Numerical Methods for Solving the Time-Space Fractional Diffusion Equation in Two Dimensions
SIAM Journal on Scientific Computing
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Journal of Computational Physics
Jacobian-predictor-corrector approach for fractional differential equations
Advances in Computational Mathematics
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Fractional differential equations are increasingly used to model problems in acoustics and thermal systems, rheology and modelling of materials and mechanical systems, signal processing and systems identification, control and robotics, and other areas of application. This paper further analyses the underlying structure of fractional differential equations. From a new point of view, we apprehend the short memory principle of fractional calculus and farther apply a Adams-type predictor-corrector approach for the numerical solution of fractional differential equation. And the detailed error analysis is presented. Combining the short memory principle and the predictor-corrector approach, we gain a good numerical approximation of the true solution of fractional differential equation at reasonable computational cost. A numerical example is provided and compared with the exact analytical solution for illustrating the effectiveness of the short memory principle.