Well-posedness of fractional differential equations with variable-order Caputo-Fabrizio derivative

Xiangcheng Zheng, Hong Wang and Hongfei Fu

Chaos, Solitons & Fractals, 2020, vol. 138, issue C

Abstract: We propose a nonlinear fractional ordinary differential equation (FODE) with variable-order Caputo-Fabrizio derivative, denoted by VO-CF-FODE, and prove its well-posedness. In particular, we prove that when the variable order is an integer at the initial time, the well-posedness of the proposed model does not require additional conditions imposed on the coefficient and the source term that is common in the context of constant-order CF-FODEs. The proposed methods are further extended to prove some well-posedness results of the corresponding linear partial differential equations.

Keywords: Caputo-Fabrizio derivative; Variable-order; Fractional differential equations; Well-posedness (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:138:y:2020:i:c:s0960077920303659

DOI: 10.1016/j.chaos.2020.109966

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