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Volume 5, Issue 3
Well-Posedness for Fractional $(p, q)$-Difference Equations Initial Value Problem

Mi Zhou

DOI: 10.12150/jnma.2023.565

J. Nonl. Mod. Anal., 5 (2023), pp. 565-579.

Published online: 2023-08

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

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  • Abstract

In this paper, we investigate a class of the fractional $(p, q)$-difference initial value problem with the fractional $(p, q)$-integral boundary conditions with the aid of the method of successive approximations(Picard method) and fractional $(p, q)$-Gronwall inequality, obtaining sufficient conditions for the existence, uniqueness and continuous dependence results of solutions.

  • Keywords

Well-posedness, fractional $(p, q)$-difference equation, initial value problem, fractional $(p, q)$-Gronwall inequality.

  • AMS Subject Headings

26A33, 34A12, 39A70

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JNMA-5-565, author = {Zhou , Mi}, title = {Well-Posedness for Fractional $(p, q)$-Difference Equations Initial Value Problem}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2023}, volume = {5}, number = {3}, pages = {565--579}, abstract = {

In this paper, we investigate a class of the fractional $(p, q)$-difference initial value problem with the fractional $(p, q)$-integral boundary conditions with the aid of the method of successive approximations(Picard method) and fractional $(p, q)$-Gronwall inequality, obtaining sufficient conditions for the existence, uniqueness and continuous dependence results of solutions.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2023.565}, url = {http://global-sci.org/intro/article_detail/jnma/21952.html} }
TY - JOUR T1 - Well-Posedness for Fractional $(p, q)$-Difference Equations Initial Value Problem AU - Zhou , Mi JO - Journal of Nonlinear Modeling and Analysis VL - 3 SP - 565 EP - 579 PY - 2023 DA - 2023/08 SN - 5 DO - http://doi.org/10.12150/jnma.2023.565 UR - https://global-sci.org/intro/article_detail/jnma/21952.html KW - Well-posedness, fractional $(p, q)$-difference equation, initial value problem, fractional $(p, q)$-Gronwall inequality. AB -

In this paper, we investigate a class of the fractional $(p, q)$-difference initial value problem with the fractional $(p, q)$-integral boundary conditions with the aid of the method of successive approximations(Picard method) and fractional $(p, q)$-Gronwall inequality, obtaining sufficient conditions for the existence, uniqueness and continuous dependence results of solutions.

Mi Zhou. (2023). Well-Posedness for Fractional $(p, q)$-Difference Equations Initial Value Problem. Journal of Nonlinear Modeling and Analysis. 5 (3). 565-579. doi:10.12150/jnma.2023.565
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