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A Generalized q -Mittag-Leffler Function by q -Captuo Fractional Linear Equations

Author

Listed:
  • Thabet Abdeljawad
  • Betül Benli
  • Dumitru Baleanu

Abstract

Some Caputo q -fractional difference equations are solved. The solutions are expressed by means of a new introduced generalized type of q -Mittag-Leffler functions. The method of successive approximation is used to obtain the solutions. The obtained q -version of Mittag-Leffler function is thought as the q -analogue of the one introduced previously by Kilbas and Saigo (1995).

Suggested Citation

  • 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.
    • Handle: RePEc:hin:jnlaaa:546062
    DOI: 10.1155/2012/546062
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    Cited by:

    1. Wengui Yang & Yaping Qin, 2016. "Positive Solutions for Nonlinear Caputo Type Fractional q -Difference Equations with Integral Boundary Conditions," Mathematics, MDPI, vol. 4(4), pages 1-15, November.
    2. Mouataz Billah Mesmouli & Abdelouaheb Ardjouni, 2022. "Stability in Nonlinear Neutral Caputo q -Fractional Difference Equations," Mathematics, MDPI, vol. 10(24), pages 1-9, December.
    3. 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.
    4. Basheer, Saeed F.A. & Marabeh, Mohammad A.A., 2023. "Fuzzy Caputo q-fractional linear equations on the time scale Tq," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).

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