Regularity for a non-local diffusion equation with Riemann-Liouville derivative-Reference-Cited by-同舟云学术

Regularity for a non-local diffusion equation with Riemann-Liouville derivative

Published:2023 Issue:Spec. issue 1 Volume:27 Page:373-382
ISSN:0354-9836
Container-title:Thermal Science
language:en
Short-container-title:THERM SCI

Author:

Tuan Nguyen¹,Kumar Devendra²,Nguyen Anh³

Affiliation:

1. Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam + Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam

2. Department of Mathematics, University of Rajasthan, Jaipur, Rajasthan, India

3. Division of Applied Mathematics, Science and Technology Advanced Institute, Van Lang University, Ho Chi Minh City, Vietnam + Faculty of Applied Technology, School of Technology, Van Lang University, Ho Chi Minh City, Vietnam

Abstract

Our main goal in this paper is to investigate the regularity of the mild solution fractional diffusion equation which can be used in the modelling of heat transfer with memory effects. Under some various assumptions of the input data, we obtain two main results. We also provide the upper bound and lower bound of the source function. The main tool is to use complex evaluations involving the Wright function.

Publisher

National Library of Serbia

Subject

Renewable Energy, Sustainability and the Environment

Reference18 articles.

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3. Zhou, Y., Basic Theory of Fractional Differential Equations, World Scientific, Singapore, Singapore, 2014

4. Chen, Z. Q., , et al., Fractional Time Stochastic Partial Differential Equations, Stochastic Processes and their Applications, 125 (2015), 4, pp. 1470-1499

5. He, J. H., Ji, F. Y., Two-Scale Mathematics and Fractional Calculus for Thermodynamics, Thermal Science, 23 (2019), 4, pp. 2131-2133

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