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Volume 6, Issue 3
Unique Solution for a General Coupled System of Fractional Differential Equations

Mengjiao Zhao & Chengbo Zhai

DOI: 10.12150/jnma.2024.746

J. Nonl. Mod. Anal., 6 (2024), pp. 746-758.

Published online: 2024-08

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

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  • Abstract

This paper discusses a new coupled system of Riemann-Liouville fractional differential equations, in which the nonlinear terms include the Riemann-Liouville fractional integrals and the boundary value problems involve three-points. We seek also for the existence and uniqueness of solutions for this new system. We first get some useful properties of the Green’s function generated by the system, and then we apply a fixed point theorem of increasing $φ$-$(h, e)$-concave operators to this new coupled system. Finally, we gain the existence and uniqueness results of the solution for this problem. In the end, a concrete example is structured to illustrate the main result.

  • Keywords

Existence and uniqueness, coupled system of fractional differential equations, fixed point theorem, $φ$-$(h, e)$-concave operators.

  • AMS Subject Headings

26A33, 34B15

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{JNMA-6-746, author = {Zhao , Mengjiao and Zhai , Chengbo}, title = {Unique Solution for a General Coupled System of Fractional Differential Equations}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2024}, volume = {6}, number = {3}, pages = {746--758}, abstract = {

This paper discusses a new coupled system of Riemann-Liouville fractional differential equations, in which the nonlinear terms include the Riemann-Liouville fractional integrals and the boundary value problems involve three-points. We seek also for the existence and uniqueness of solutions for this new system. We first get some useful properties of the Green’s function generated by the system, and then we apply a fixed point theorem of increasing $φ$-$(h, e)$-concave operators to this new coupled system. Finally, we gain the existence and uniqueness results of the solution for this problem. In the end, a concrete example is structured to illustrate the main result.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2024.746}, url = {http://global-sci.org/intro/article_detail/jnma/23360.html} }
TY - JOUR T1 - Unique Solution for a General Coupled System of Fractional Differential Equations AU - Zhao , Mengjiao AU - Zhai , Chengbo JO - Journal of Nonlinear Modeling and Analysis VL - 3 SP - 746 EP - 758 PY - 2024 DA - 2024/08 SN - 6 DO - http://doi.org/10.12150/jnma.2024.746 UR - https://global-sci.org/intro/article_detail/jnma/23360.html KW - Existence and uniqueness, coupled system of fractional differential equations, fixed point theorem, $φ$-$(h, e)$-concave operators. AB -

This paper discusses a new coupled system of Riemann-Liouville fractional differential equations, in which the nonlinear terms include the Riemann-Liouville fractional integrals and the boundary value problems involve three-points. We seek also for the existence and uniqueness of solutions for this new system. We first get some useful properties of the Green’s function generated by the system, and then we apply a fixed point theorem of increasing $φ$-$(h, e)$-concave operators to this new coupled system. Finally, we gain the existence and uniqueness results of the solution for this problem. In the end, a concrete example is structured to illustrate the main result.

Zhao , Mengjiao and Zhai , Chengbo. (2024). Unique Solution for a General Coupled System of Fractional Differential Equations. Journal of Nonlinear Modeling and Analysis. 6 (3). 746-758. doi:10.12150/jnma.2024.746
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