Math. Model. Nat. Phenom.
Volume 16, 2021
Fractional Dynamics in Natural Phenomena
|Number of page(s)||14|
|Published online||28 April 2021|
Initial value problem for fractional Volterra integrodifferential pseudo-parabolic equations
Faculty of Fundamental Science, Industrial University of Ho Chi Minh City, Vietnam.
2 Division of Applied Mathematics, Thu Dau Mot University, Binh Duong Province, Vietnam.
3 Department of Mathematics, University of Rajasthan, Jaipur 302004, Rajasthan, India.
4 Division of Applied Mathematics, Thu Dau Mot University, Binh Duong Province, Vietnam.
* Corresponding author: email@example.com
Accepted: 28 February 2021
In this paper, we investigate a initial value problem for the Caputo time-fractional pseudo-parabolic equations with fractional Laplace operator of order 0 < ν ≤ 1 and the nonlinear memory source term. For 0 < ν < 1, the problem will be considered on a bounded domain of ℝd. By some Sobolev embeddings and the properties of the Mittag-Leffler function, we will give some results on the existence and the uniqueness of mild solution for problem (1.1) below. When ν = 1, we will introduce some Lp − Lq estimates, and based on them we derive the global existence of a mild solution in the whole space ℝd.
Mathematics Subject Classification: 26A33 / 35R11
Key words: Fractional partial differential equation / Caputo fractional / well-posedness / pseudo-parabolic equation
© The authors. Published by EDP Sciences, 2021
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