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

被引：117
作者：
Solis-Perez, J. E. [1 ]
Gomez-Aguilar, J. F. [2 ]
Atangana, A. [3 ]
机构：
[1] Tecnol Nacl Mexico, CENIDET, Interior Internado Palmira S-N, Cuernavaca 62490, Morelos, Mexico
[2] Tecnol Nacl Mexico, CONACyT, CENIDET, Interior Internado Palmira S-N, Cuernavaca 62490, Morelos, Mexico
[3] Univ Free State, Fac Nat & Agr Sci, Inst Groundwater Studies, ZA-9300 Bloemfontein, South Africa
来源：
CHAOS SOLITONS & FRACTALS | 2018年 / 114卷
关键词：
Variable-order fractional derivatives; Atangana-Toufik numerical scheme; Financial system; Memcapacitor-based circuit; MODEL; DIFFUSION; SYSTEM; DERIVATIVES; KERNEL;
D O I：
10.1016/j.chaos.2018.06.032
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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. (C) 2018 Elsevier Ltd. All rights reserved.
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页码：175 / 185
页数：11
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