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Volume 4, Issue 4
Existence and Uniqueness of Solutions for the Initial Value Problem of Fractional $q_k$-Difference Equations for Impulsive with Varying Orders

Lulu Zhang, Fanjun Li & Zhenlai Han

DOI: 10.12150/jnma.2022.701

J. Nonl. Mod. Anal., 4 (2022), pp. 701-721.

Published online: 2023-08

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

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  • Abstract

The paper studies the existence and uniqueness for impulsive fractional $q_k$-difference equations of initial value problems involving Riemann-Liouville fractional $q_k$-integral and $q_k$-derivative by defining a new $q$-shifting operator. In this paper, we obtain existence and uniqueness results for impulsive fractional $q_k$-difference equations of initial value problems by using the Schaefer’s fixed point theorem and Banach contraction mapping principle. In addition, the main result is illustrated with the aid of several examples.

  • Keywords

Impulsive fractional $q_k$-difference equation, Boundary value problem, Existence, Uniqueness.

  • AMS Subject Headings

26A33, 39A13, 34A37, 65L10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JNMA-4-701, author = {Zhang , LuluLi , Fanjun and Han , Zhenlai}, title = {Existence and Uniqueness of Solutions for the Initial Value Problem of Fractional $q_k$-Difference Equations for Impulsive with Varying Orders}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2023}, volume = {4}, number = {4}, pages = {701--721}, abstract = {

The paper studies the existence and uniqueness for impulsive fractional $q_k$-difference equations of initial value problems involving Riemann-Liouville fractional $q_k$-integral and $q_k$-derivative by defining a new $q$-shifting operator. In this paper, we obtain existence and uniqueness results for impulsive fractional $q_k$-difference equations of initial value problems by using the Schaefer’s fixed point theorem and Banach contraction mapping principle. In addition, the main result is illustrated with the aid of several examples.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2022.701}, url = {http://global-sci.org/intro/article_detail/jnma/21907.html} }
TY - JOUR T1 - Existence and Uniqueness of Solutions for the Initial Value Problem of Fractional $q_k$-Difference Equations for Impulsive with Varying Orders AU - Zhang , Lulu AU - Li , Fanjun AU - Han , Zhenlai JO - Journal of Nonlinear Modeling and Analysis VL - 4 SP - 701 EP - 721 PY - 2023 DA - 2023/08 SN - 4 DO - http://doi.org/10.12150/jnma.2022.701 UR - https://global-sci.org/intro/article_detail/jnma/21907.html KW - Impulsive fractional $q_k$-difference equation, Boundary value problem, Existence, Uniqueness. AB -

The paper studies the existence and uniqueness for impulsive fractional $q_k$-difference equations of initial value problems involving Riemann-Liouville fractional $q_k$-integral and $q_k$-derivative by defining a new $q$-shifting operator. In this paper, we obtain existence and uniqueness results for impulsive fractional $q_k$-difference equations of initial value problems by using the Schaefer’s fixed point theorem and Banach contraction mapping principle. In addition, the main result is illustrated with the aid of several examples.

Lulu Zhang, Fanjun Li & Zhenlai Han. (2023). Existence and Uniqueness of Solutions for the Initial Value Problem of Fractional $q_k$-Difference Equations for Impulsive with Varying Orders. Journal of Nonlinear Modeling and Analysis. 4 (4). 701-721. doi:10.12150/jnma.2022.701
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