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Volume 3, Issue 4
Solvability and Stability for Singular Fractional $(p, q)$-Difference Equation

Zhongyun Qin & Shurong Sun

DOI: 10.12150/jnma.2021.647

J. Nonl. Mod. Anal., 3 (2021), pp. 647-661.

Published online: 2022-06

[An open-access article; the PDF is free to any online user.]

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  • Abstract

In this paper, we initiate the solvability and stability for a class of singular fractional $(p, q)$-difference equations. First, we obtain an existence theorem of solution for the fractional $(p, q)$-difference equation. Then, by using a fractional $(p, q)$-Gronwall inequality, some stability criteria of solution are established, which also implies the uniqueness of solution.

  • Keywords

Fractional $(p, q)$-difference equation, Existence of solution, Stability, $(p, q)$-Gronwall inequality, Uniqueness.

  • AMS Subject Headings

34A12, 39A30, 39A70

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JNMA-3-647, author = {Qin , Zhongyun and Sun , Shurong}, title = {Solvability and Stability for Singular Fractional $(p, q)$-Difference Equation}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2022}, volume = {3}, number = {4}, pages = {647--661}, abstract = {

In this paper, we initiate the solvability and stability for a class of singular fractional $(p, q)$-difference equations. First, we obtain an existence theorem of solution for the fractional $(p, q)$-difference equation. Then, by using a fractional $(p, q)$-Gronwall inequality, some stability criteria of solution are established, which also implies the uniqueness of solution.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2021.647}, url = {http://global-sci.org/intro/article_detail/jnma/20688.html} }
TY - JOUR T1 - Solvability and Stability for Singular Fractional $(p, q)$-Difference Equation AU - Qin , Zhongyun AU - Sun , Shurong JO - Journal of Nonlinear Modeling and Analysis VL - 4 SP - 647 EP - 661 PY - 2022 DA - 2022/06 SN - 3 DO - http://doi.org/10.12150/jnma.2021.647 UR - https://global-sci.org/intro/article_detail/jnma/20688.html KW - Fractional $(p, q)$-difference equation, Existence of solution, Stability, $(p, q)$-Gronwall inequality, Uniqueness. AB -

In this paper, we initiate the solvability and stability for a class of singular fractional $(p, q)$-difference equations. First, we obtain an existence theorem of solution for the fractional $(p, q)$-difference equation. Then, by using a fractional $(p, q)$-Gronwall inequality, some stability criteria of solution are established, which also implies the uniqueness of solution.

Zhongyun Qin & Shurong Sun. (2022). Solvability and Stability for Singular Fractional $(p, q)$-Difference Equation. Journal of Nonlinear Modeling and Analysis. 3 (4). 647-661. doi:10.12150/jnma.2021.647
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