Novel numerical method for solving variable-order fractional differential equations with power, exponential and Mittag-Leffler laws

By J. E. Solís-Pérez, José Francisco Gómez‐Aguilar, Abdon Atangana. Chaos, Solitons & Fractals, 2018

147 citations recorded by the source corpus.

Abstract Variable-order differential operators can be employed as a powerful tool to modeling nonlinear fractional differential equations and chaotical systems. In this paper, we propose a new generalize numerical schemes for simulating variable-order fractional differential operators with power-law, exponential-law and Mittag-Leffler kernel. The numerical schemes are based on the fundamental theorem of fractional calculus and the Lagrange polynomial interpolation. These schemes were applied to simulate the chaotic financial system and memcapacitor-based circuit chaotic oscillator. Numerical examples are presented to show the applicability and efficiency of this novel method.

Subfields: Control and Systems Engineering, Modeling and Simulation, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/359c6ce573038b5ca53ea93a31d5527af845b08b

How researchers see this paper

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In Control and Systems Engineering

1. Yong Zhang
2. Wen Chen
3. Hongguang Sun
4. A. Chang

In Modeling and Simulation

1. Yong Zhang
2. A. Chang
3. Wen Chen
4. Hongguang Sun
5. Dumitru Băleanu
6. Arran Fernandez
7. Ali H. Bhrawy
8. M. A. Zaky

In Statistical and Nonlinear Physics

1. A. Chang
2. Wen Chen
3. Yong Zhang
4. Hongguang Sun

Citations in the corpus

• A review on variable-order fractional differential equations: mathematical foundations, physical models, numerical methods and applications (2019, methodology): “In addition, the VO fractional operator has also been used in other non-local definitions with non-singular kernels, which is beyond the scope of this review [99, 127].”