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Volume 5, Issue 4
Existence Results for the Higher-Order Weighted Caputo-Fabrizio Fractional Derivative

Chunshuo Li, Qing Zhang & Qiaoluan Li

DOI: 10.12150/jnma.2023.763

J. Nonl. Mod. Anal., 5 (2023), pp. 763-781.

Published online: 2023-12

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

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  • Abstract

By the definition of the higher-order fractional derivative, we explore the central properties of the higher-order Caputo-Fabrizio fractional derivative and integral with a weighted term. Furthermore, by dint of Schaefer’s fixed point theorem, $α$-$\psi$-Contraction theorem, etc., we establish the existence of solutions for nonlinear equations. We also give three examples to make our main conclusion clear.

  • Keywords

Higher-order weighted fractional derivative, Caputo-Fabrizio derivative, existence.

  • AMS Subject Headings

26A33, 35A01, 47H10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JNMA-5-763, author = {Li , ChunshuoZhang , Qing and Li , Qiaoluan}, title = {Existence Results for the Higher-Order Weighted Caputo-Fabrizio Fractional Derivative}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2023}, volume = {5}, number = {4}, pages = {763--781}, abstract = {

By the definition of the higher-order fractional derivative, we explore the central properties of the higher-order Caputo-Fabrizio fractional derivative and integral with a weighted term. Furthermore, by dint of Schaefer’s fixed point theorem, $α$-$\psi$-Contraction theorem, etc., we establish the existence of solutions for nonlinear equations. We also give three examples to make our main conclusion clear.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2023.763}, url = {http://global-sci.org/intro/article_detail/jnma/22207.html} }
TY - JOUR T1 - Existence Results for the Higher-Order Weighted Caputo-Fabrizio Fractional Derivative AU - Li , Chunshuo AU - Zhang , Qing AU - Li , Qiaoluan JO - Journal of Nonlinear Modeling and Analysis VL - 4 SP - 763 EP - 781 PY - 2023 DA - 2023/12 SN - 5 DO - http://doi.org/10.12150/jnma.2023.763 UR - https://global-sci.org/intro/article_detail/jnma/22207.html KW - Higher-order weighted fractional derivative, Caputo-Fabrizio derivative, existence. AB -

By the definition of the higher-order fractional derivative, we explore the central properties of the higher-order Caputo-Fabrizio fractional derivative and integral with a weighted term. Furthermore, by dint of Schaefer’s fixed point theorem, $α$-$\psi$-Contraction theorem, etc., we establish the existence of solutions for nonlinear equations. We also give three examples to make our main conclusion clear.

Chunshuo Li, Qing Zhang & Qiaoluan Li. (2023). Existence Results for the Higher-Order Weighted Caputo-Fabrizio Fractional Derivative. Journal of Nonlinear Modeling and Analysis. 5 (4). 763-781. doi:10.12150/jnma.2023.763
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