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

Ala Eddine Taier; Ranchao Wu; Naveed Iqbal; Sijjad Ali

doi:doi:10.11648/j.acm.20241304.13

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

Ala Eddine Taier^*, Ranchao Wu, Naveed Iqbal, Sijjad Ali

Published in Applied and Computational Mathematics (Volume 13, Issue 4)

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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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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TY  - JOUR
T1  - The Existence and Uniqueness Results of Solutions for a Fractional Hybrid Integro-differential System
AU  - Ala Eddine Taier
AU  - Ranchao Wu
AU  - Naveed Iqbal
AU  - Sijjad Ali
Y1  - 2024/08/07
PY  - 2024
N1  - https://doi.org/10.11648/j.acm.20241304.13
DO  - 10.11648/j.acm.20241304.13
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
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EP  - 104
PB  - Science Publishing Group
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UR  - https://doi.org/10.11648/j.acm.20241304.13
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.
VL  - 13
IS  - 4
ER  -

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Author Information

Ala Eddine Taier

Department of Applied Mathematics, Anhui University, Hefei, China

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Ranchao Wu

Department of Applied Mathematics, Anhui University, Hefei, China

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Naveed Iqbal

Department of Mathematics, University of Ha’il, Ha’il, Saudi Arabia

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Sijjad Ali

College of Computer Science and Software Engineering, Shenzhen University, Shenzhen, China

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Plain Text BibTeX RIS

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

Copy | Download

@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}
}

Copy | Download

TY  - JOUR
T1  - The Existence and Uniqueness Results of Solutions for a Fractional Hybrid Integro-differential System
AU  - Ala Eddine Taier
AU  - Ranchao Wu
AU  - Naveed Iqbal
AU  - Sijjad Ali
Y1  - 2024/08/07
PY  - 2024
N1  - https://doi.org/10.11648/j.acm.20241304.13
DO  - 10.11648/j.acm.20241304.13
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 94
EP  - 104
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20241304.13
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.
VL  - 13
IS  - 4
ER  -

Copy | Download