Author:
Ngoc Tran Bao,Tuan Nguyen Huy,Sakthivel R.,O'Regan Donal
Abstract
<p style='text-indent:20px;'>In this paper, we consider a nonlinear fractional diffusion equations with a Riemann-Liouville derivative. First, we establish the global existence and uniqueness of mild solutions under some assumptions on the input data. Some regularity results for the mild solution and its derivatives of fractional orders are also derived. Our key idea is to combine the theories of Mittag-Leffler functions, Banach fixed point theorem and some Sobolev embeddings.</p>
Publisher
American Institute of Mathematical Sciences (AIMS)
Subject
Applied Mathematics,Control and Optimization,Modeling and Simulation
Reference30 articles.
1. E. A. Abdel-Rehim.From power laws to fractional diffusion processes with and without external forces, the non direct way., Fract. Calc. Appl. Anal., 22 (2019), 60-77.
2. M. Abramowitz and I. A. Stegun, Table Errata: Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Dover, New York, 1972.
3. E. Alvarez, G. Ciprian, V. Keyantuo, M. Warma.Well-posedness results for a class of semi-linear super-diffusive equations, Nonlinear Anal., 181 (2019), 24-61.
4. L. Banjai, E. Otárola.A PDE approach to fractional diffusion: A space-fractional wave equation, Numer. Math., 143 (2019), 177-222.
5. M. Benchohra, S. Bouriah, J. J. Nieto.Existence and Ulam stability for nonlinear implicit differential equations with Riemann-Liouville fractional derivative, Demonstr. Math., 52 (2019), 437-450.