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The Existence and Uniqueness Results of Solutions for a Fractional Hybrid Integro-differential System

Received: 3 March 2024     Accepted: 22 April 2024     Published: 7 August 2024
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Abstract

This paper discuss two important results for a fractional hybrid boundary value problem of Riemann-Liouville integro-differential systems, the researches and the advance in this field and also the importance of this subject in the modeling of nonlinear real phenomena corresponding to a great variety of events gives the motivation to study this boundary value problem. The results are as follow, the first result consider the existence and uniqueness results of solutions for a fractional hybrid boundary value problem of Riemann-Liouville integro-differential system this result based on Krasnoslskii fixed point theorem for a sum of two operators, the second result is the uniqueness of solution for fractional hybrid boundary value problem of Riemann-Liouville integro-differential systems, the main result is based on Banach fixed point theorem, both results comes after transforming the system into Volterra integral system then transform again into operator system, then using fixed point theory to prove the results, this articule was ended buy an example to well illustrat the results and ideas of proof.

Published in Applied and Computational Mathematics (Volume 13, Issue 4)
DOI 10.11648/j.acm.20241304.13
Page(s) 94-104
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Hybrid Fixed Point Theorem, Banach Algebra, Operators Equations

References
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Cite This Article
  • APA Style

    Taier, A. E., Wu, R., Iqbal, N., Ali, S. (2024). The Existence and Uniqueness Results of Solutions for a Fractional Hybrid Integro-differential System. Applied and Computational Mathematics, 13(4), 94-104. https://doi.org/10.11648/j.acm.20241304.13

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    ACS Style

    Taier, A. E.; Wu, R.; Iqbal, N.; Ali, S. The Existence and Uniqueness Results of Solutions for a Fractional Hybrid Integro-differential System. Appl. Comput. Math. 2024, 13(4), 94-104. doi: 10.11648/j.acm.20241304.13

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    AMA Style

    Taier AE, Wu R, Iqbal N, Ali S. The Existence and Uniqueness Results of Solutions for a Fractional Hybrid Integro-differential System. Appl Comput Math. 2024;13(4):94-104. doi: 10.11648/j.acm.20241304.13

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  • @article{10.11648/j.acm.20241304.13,
      author = {Ala Eddine Taier and Ranchao Wu and Naveed Iqbal and Sijjad Ali},
      title = {The Existence and Uniqueness Results of Solutions for a Fractional Hybrid Integro-differential System},
      journal = {Applied and Computational Mathematics},
      volume = {13},
      number = {4},
      pages = {94-104},
      doi = {10.11648/j.acm.20241304.13},
      url = {https://doi.org/10.11648/j.acm.20241304.13},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20241304.13},
      abstract = {This paper discuss two important results for a fractional hybrid boundary value problem of Riemann-Liouville integro-differential systems, the researches and the advance in this field and also the importance of this subject in the modeling of nonlinear real phenomena corresponding to a great variety of events gives the motivation to study this boundary value problem. The results are as follow, the first result consider the existence and uniqueness results of solutions for a fractional hybrid boundary value problem of Riemann-Liouville integro-differential system this result based on Krasnoslskii fixed point theorem for a sum of two operators, the second result is the uniqueness of solution for fractional hybrid boundary value problem of Riemann-Liouville integro-differential systems, the main result is based on Banach fixed point theorem, both results comes after transforming the system into Volterra integral system then transform again into operator system, then using fixed point theory to prove the results, this articule was ended buy an example to well illustrat the results and ideas of proof.},
     year = {2024}
    }
    

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    AU  - Ala Eddine Taier
    AU  - Ranchao Wu
    AU  - Naveed Iqbal
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    DO  - 10.11648/j.acm.20241304.13
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    JF  - Applied and Computational Mathematics
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    AB  - This paper discuss two important results for a fractional hybrid boundary value problem of Riemann-Liouville integro-differential systems, the researches and the advance in this field and also the importance of this subject in the modeling of nonlinear real phenomena corresponding to a great variety of events gives the motivation to study this boundary value problem. The results are as follow, the first result consider the existence and uniqueness results of solutions for a fractional hybrid boundary value problem of Riemann-Liouville integro-differential system this result based on Krasnoslskii fixed point theorem for a sum of two operators, the second result is the uniqueness of solution for fractional hybrid boundary value problem of Riemann-Liouville integro-differential systems, the main result is based on Banach fixed point theorem, both results comes after transforming the system into Volterra integral system then transform again into operator system, then using fixed point theory to prove the results, this articule was ended buy an example to well illustrat the results and ideas of proof.
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