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

J.E. Solís-Pérez, J.F. Gómez-Aguilar and A. Atangana

Chaos, Solitons & Fractals, 2018, vol. 114, issue C, 175-185

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.

Keywords: Variable-order fractional derivatives; Atangana–Toufik numerical scheme; Financial system; Memcapacitor-based circuit (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (17)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:114:y:2018:i:c:p:175-185

DOI: 10.1016/j.chaos.2018.06.032

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