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A remark on the q-fractional order differential equations

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  • Tang, Yongchao
  • Zhang, Tie

Abstract

An analytical method to obtain the exact solution of q-fractional order differential equations was presented in article Koca (2015) which shows that: “Solving a q-fractional order differential equation is equivalent to solve a q-integer order differential equation”. In this article, we first show that the analytical method given in [3] is wrong. Then, we propose analytical and numerical methods for the Caputo type q-fractional differential equations by using the q-beta function. Some examples are given to disconfirm the solving method in [3] and valid the effectiveness of our methods.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:350:y:2019:i:c:p:198-208
    DOI: 10.1016/j.amc.2019.01.008
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    References listed on IDEAS

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    1. Koca, Ilknur, 2015. "A method for solving differential equations of q-fractional order," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 1-5.
    2. Thabet Abdeljawad & Betül Benli & Dumitru Baleanu, 2012. "A Generalized q -Mittag-Leffler Function by q -Captuo Fractional Linear Equations," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-11, May.
    3. Huiqin Chen & Shugui Kang & Lili Kong & Ying Gao, 2018. "Existence of Three Positive Solutions for a Class of Boundary Value Problems of Caputo Fractional -Difference Equation," Discrete Dynamics in Nature and Society, Hindawi, vol. 2018, pages 1-9, February.
    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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    1. Muhammad Naeem & Saqib Hussain & Shahid Khan & Tahir Mahmood & Maslina Darus & Zahid Shareef, 2020. "Janowski Type q -Convex and q -Close-to-Convex Functions Associated with q -Conic Domain," Mathematics, MDPI, vol. 8(3), pages 1-13, March.

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