Math. Model. Nat. Phenom.
Volume 16, 2021
Fractional Dynamics in Natural Phenomena
|Number of page(s)||21|
|Published online||23 March 2021|
On the initial value problem for fractional Volterra integrodifferential equations with a Caputo–Fabrizio derivative
Applied Analysis Research Group, Faculty of Mathematics and Statistics, Ton Duc Thang University,
Ho Chi Minh City, Vietnam.
2 Division of Applied Mathematics, Thu Dau Mot University, Binh Duong Province, Vietnam.
3 School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland.
* Corresponding author: firstname.lastname@example.org
Accepted: 24 January 2021
In this paper, a time-fractional integrodifferential equation with the Caputo–Fabrizio type derivative will be considered. The Banach fixed point theorem is the main tool used to extend the results of a recent paper of Tuan and Zhou [J. Comput. Appl. Math. 375 (2020) 112811]. In the case of a globally Lipschitz source terms, thanks to the Lp − Lq estimate method, we establish global in time well-posed results for mild solution. For the case of locally Lipschitz terms, we present existence and uniqueness results. Also, we show that our solution will blow up at a finite time. Finally, we present some numerical examples to illustrate the regularity and continuation of the solution based on the time variable.
Mathematics Subject Classification: 26A33 / 35B65 / 35R11
Key words: Fractional nonclassical diffusion equation / well-posednes / regularity estimates
© The authors. Published by EDP Sciences, 2021
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