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The Multi-scale Method for Solving Nonlinear Time Space Fractional Partial Differential Equations

IEEE/CAA Journal of Automatica Sinica 2019年第1期6卷 299-306页

作者： Hossein Aminikhah Mahdieh Tahmasebi Mahmoud Mohammadi Roozbahani the Department of Applied Mathematics University of Guilan the Department of Applied Mathematics Faculty of Mathematical SciencesTarbiat Modares University

In this paper, we present a new algorithm to solve a kind of nonlinear time space-fractional partial differential equations on a finite domain. The method is based on B-spline wavelets approximations, some of these functions are reshaped to satisfy on boundary conditions exactly. The Adams fractional method is used to reduce the problem to a system of equations. By multiscale method this system is divided into some smaller systems which have less computations. We get an approximated solution which is more accurate on some subdomains by combining the solutions of these systems. Illustrative examples are included to demonstrate the validity and applicability of our proposed technique, also the stability of the method is discussed.

关键词： Adams fractional method B-spline wavelets multi-scale method nonlinear fractional partial differential equations

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Numerical Solution of the Distributed-Order Fractional Bagley-Torvik Equation

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IEEE/CAA Journal of Automatica Sinica 2019年第3期6卷 760-765页

作者： Hossein Aminikhah Amir Hosein Refahi Sheikhani Tahereh Houlari Hadi Rezazadeh the Department of Applied Mathematics Faculty of Mathematical Sciences University of Guilan the Department of Applied Mathematics Faculty of Mathematical Sciences Islamic Azad University Lahijan Branch the Faculty of Engineering Technology Amol University of Special Modern Technologies Department of Applied Mathematics University of Guilan

In this paper, two numerical methods are proposed for solving distributed-order fractional Bagley-Torvik equation.This equation is used in modeling the motion of a rigid plate immersed in a Newtonian fluid with respect to the nonnegative density function. Using the composite Boole's rule the distributedorder Bagley-Torvik equation is approximated by a multi-term time-fractional equation, which is then solved by the GrunwaldLetnikov method(GLM) and the fractional differential transform method(FDTM). Finally, we compared our results with the exact results of some cases and show the excellent agreement between the approximate result and the exact solution.

关键词： Bagley-Torvik equation distributed-order fractional fractional differential transform method Grunwald- Letnikov method

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