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A method for solving differential equations of q-fractional order

Author

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  • Koca, Ilknur

Abstract

In this work, we considered the q-differential equations of order 0 < q < 1 with initial condition x(0)=x0. The derivative with fractional order considered here is the Caputo time since it allows the use of initial conditions. An analytical method to obtain exact solution of this class of fractional differential equations is provided. Some illustrative examples are provided to underpin and illustrate the efficiency of the used method.

Suggested Citation

  • Koca, Ilknur, 2015. "A method for solving differential equations of q-fractional order," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 1-5.
    • Handle: RePEc:eee:apmaco:v:266:y:2015:i:c:p:1-5
    DOI: 10.1016/j.amc.2015.05.049
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    Cited by:

    1. Algahtani, Obaid Jefain Julaighim, 2016. "Comparing the Atangana–Baleanu and Caputo–Fabrizio derivative with fractional order: Allen Cahn model," Chaos, Solitons & Fractals, Elsevier, vol. 89(C), pages 552-559.
    2. Tang, Yongchao & Zhang, Tie, 2019. "A remark on the q-fractional order differential equations," Applied Mathematics and Computation, Elsevier, vol. 350(C), pages 198-208.
    3. Yusuf, Abdullahi & Inc, Mustafa & Isa Aliyu, Aliyu & Baleanu, Dumitru, 2018. "Efficiency of the new fractional derivative with nonsingular Mittag-Leffler kernel to some nonlinear partial differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 220-226.
    4. Alkahtani, Badr Saad T. & Atangana, Abdon, 2016. "Analysis of non-homogeneous heat model with new trend of derivative with fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 89(C), pages 566-571.

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