Fractal-fractional differentiation and integration: Connecting fractal calculus and fractional calculus to predict complex system

Abdon Atangana

Chaos, Solitons & Fractals, 2017, vol. 102, issue C, 396-406

Abstract: New operators of differentiation have been introduced in this paper as convolution of power law, exponential decay law, and generalized Mittag-Leffler law with fractal derivative. The new operators will be referred as fractal-fractional differential and integral operators. The new operators aimed to attract more non-local natural problems that display at the same time fractal behaviors. Some new properties are presented, the numerical approximation of these new operators are also presented with some applications to real world problem.

Keywords: Fractal fractional calculus; Non-locality; Non-singularity; Numerical approximation (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (75)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:102:y:2017:i:c:p:396-406

DOI: 10.1016/j.chaos.2017.04.027

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