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

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  • Zheng, Xiangcheng
  • Wang, Hong
  • Fu, Hongfei

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.

Suggested Citation

  • Zheng, Xiangcheng & Wang, Hong & Fu, Hongfei, 2020. "Well-posedness of fractional differential equations with variable-order Caputo-Fabrizio derivative," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    • Handle: RePEc:eee:chsofr:v:138:y:2020:i:c:s0960077920303659
    DOI: 10.1016/j.chaos.2020.109966
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    References listed on IDEAS

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    1. Baleanu, Dumitru & Jajarmi, Amin & Mohammadi, Hakimeh & Rezapour, Shahram, 2020. "A new study on the mathematical modelling of human liver with Caputo–Fabrizio fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    2. Huang, Jiechen & Wang, Juan & Xia, Chengyi, 2020. "Role of vaccine efficacy in the vaccination behavior under myopic update rule on complex networks," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    3. Solís-Pérez, J.E. & Gómez-Aguilar, J.F. & Atangana, A., 2018. "Novel numerical method for solving variable-order fractional differential equations with power, exponential and Mittag-Leffler laws," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 175-185.
    4. Veeresha, P. & Baskonus, Haci Mehmet & Prakasha, D.G. & Gao, Wei & Yel, Gulnur, 2020. "Regarding new numerical solution of fractional Schistosomiasis disease arising in biological phenomena," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
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    1. Oscar Martínez-Fuentes & Fidel Meléndez-Vázquez & Guillermo Fernández-Anaya & José Francisco Gómez-Aguilar, 2021. "Analysis of Fractional-Order Nonlinear Dynamic Systems with General Analytic Kernels: Lyapunov Stability and Inequalities," Mathematics, MDPI, vol. 9(17), pages 1-29, August.

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