Explicit methods for fractional differential equations and their stability properties

By Luciano Galeone, Roberto Garrappa. 2009

96 citations recorded by the source corpus.

The use of explicit methods in the numerical treatment of differential equations of fractional order is an area not yet widely investigated. In this paper stability properties of some multistep methods of explicit type are investigated and new methods with larger intervals of stability are proposed. Some numerical experiments are presented in order to validate theoretical results.

Subfields: Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/38e26f36c54670af0bc84bfc363efc8b6ee50179

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In Modeling and Simulation

1. Changpin Li
2. Ian L Turner
3. Fawang Liu
4. Fanhai Zeng
5. I. Győri
6. Jan Cermak
7. Luděk Nechvátal
8. Jigen Peng

In Numerical Analysis

1. Changpin Li
2. Ian L Turner
3. Fawang Liu
4. Fanhai Zeng
5. I. Győri
6. Jan Cermak
7. Jigen Peng
8. Luděk Nechvátal

Citations in the corpus

• OSCILLATORY BEHAVIOR OF A CLASS OF FRACTIONAL DIFFERENTIAL EQUATIONS WITH DAMPING (2013, methodology): “Many papers have investigated some aspects of fractional differential equations, such as the existence and uniqueness of solutions to Cauchy type problems, the methods for explicit and numerical solutions, and the stability of solutions, and we refer to [12–19].”
• On explicit stability conditions for a linear fractional difference system (2015, methodology): “Its study was initiated by theoretical analysis of basic numerical schemes for fractional differential equations performed in the papers [13], [14] and [18].”
• The Use of Finite Difference/Element Approaches for Solving the Time-Fractional Subdiffusion Equation (2013, background): “1), so we omit the corresponding details of s and w (β) n,k; see [15, 18, 19, 32] for more detailed information.”
• Fractional differential equations: a novel study of local and global solutions in Banach spaces (2013, unknown): “instance [11, 26, 30, 36, 41, 53, 55, 66, 67].”
• The Finite Difference Methods for Fractional Ordinary Differential Equations (2013, methodology): “In [22, 23], numerical methods of the linear multistep type were discussed and stability results were derived only for the linear equation of the form CD 0,t y(t) = y(t), ∈ .”
• A note on property of the Mittag-Leffler function (2010, background): “, [2,3,6,8]), among which the following one will perhaps receive considerable interests from the society of dynamical systems: the function t → Eα(at) solves the fractional differential equation of order α C 0 D α t x(t)= ax(t), t 0, (1.”