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Volume 6, Issue 1
Existence and Uniqueness of Solutions for Time-Fractional Oldroyd-B Fluid Equations with Generalized Fractional Derivatives

Hassan Messaoudi, Abdelouaheb Ardjouni & Salah Zitouni

DOI: 10.12150/jnma.2024.142

J. Nonl. Mod. Anal., 6 (2024), pp. 142-151.

Published online: 2024-03

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

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  • Abstract

In this paper, we study the existence and uniqueness of solutions for time-fractional Oldroyd-B fluid equations with generalized fractional derivatives. We distinguish two cases. Firstly for the linear case, we get regularity results under some hypotheses of the source function and the initial data. Secondly for the nonlinear case, we use the Banach fixed point theorem to obtain the existence and uniqueness of solutions.

  • Keywords

Time-fractional Oldroyd-B fluid equations, generalized fractional derivatives, generalized Laplace transform, regularity, Banach fixed point theorem.

  • AMS Subject Headings

35R11, 35B65, 26A33

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JNMA-6-142, author = {Messaoudi , HassanArdjouni , Abdelouaheb and Zitouni , Salah}, title = {Existence and Uniqueness of Solutions for Time-Fractional Oldroyd-B Fluid Equations with Generalized Fractional Derivatives}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2024}, volume = {6}, number = {1}, pages = {142--151}, abstract = {

In this paper, we study the existence and uniqueness of solutions for time-fractional Oldroyd-B fluid equations with generalized fractional derivatives. We distinguish two cases. Firstly for the linear case, we get regularity results under some hypotheses of the source function and the initial data. Secondly for the nonlinear case, we use the Banach fixed point theorem to obtain the existence and uniqueness of solutions.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2024.142}, url = {http://global-sci.org/intro/article_detail/jnma/22971.html} }
TY - JOUR T1 - Existence and Uniqueness of Solutions for Time-Fractional Oldroyd-B Fluid Equations with Generalized Fractional Derivatives AU - Messaoudi , Hassan AU - Ardjouni , Abdelouaheb AU - Zitouni , Salah JO - Journal of Nonlinear Modeling and Analysis VL - 1 SP - 142 EP - 151 PY - 2024 DA - 2024/03 SN - 6 DO - http://doi.org/10.12150/jnma.2024.142 UR - https://global-sci.org/intro/article_detail/jnma/22971.html KW - Time-fractional Oldroyd-B fluid equations, generalized fractional derivatives, generalized Laplace transform, regularity, Banach fixed point theorem. AB -

In this paper, we study the existence and uniqueness of solutions for time-fractional Oldroyd-B fluid equations with generalized fractional derivatives. We distinguish two cases. Firstly for the linear case, we get regularity results under some hypotheses of the source function and the initial data. Secondly for the nonlinear case, we use the Banach fixed point theorem to obtain the existence and uniqueness of solutions.

Messaoudi , HassanArdjouni , Abdelouaheb and Zitouni , Salah. (2024). Existence and Uniqueness of Solutions for Time-Fractional Oldroyd-B Fluid Equations with Generalized Fractional Derivatives. Journal of Nonlinear Modeling and Analysis. 6 (1). 142-151. doi:10.12150/jnma.2024.142
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