Monotone iterative technique for time-space fractional diffusion equations involving delay
Articles
Qiang Li
Shanxi Normal University
https://orcid.org/0000-0001-5380-7420
Guotao Wang
Shanxi Normal University
Mei Wei
Northwest Normal University
https://orcid.org/0000-0003-0140-4237
Published 2021-03-01
https://doi.org/10.15388/namc.2021.26.21656
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Keywords

time-space fractional diffusion equations
operator semigroup
monotone iterative technique
existence and uniqueness
delay

How to Cite

Li Q., Wang G. and Wei M. (2021) “Monotone iterative technique for time-space fractional diffusion equations involving delay”, Nonlinear Analysis: Modelling and Control, 26(2), pp. 241-258. doi: 10.15388/namc.2021.26.21656.

Abstract

This paper considers the initial boundary value problem for the time-space fractional delayed diffusion equation with fractional Laplacian. By using the semigroup theory of operators and the monotone iterative technique, the existence and uniqueness of mild solutions for the abstract time-space evolution equation with delay under some quasimonotone conditions are obtained. Finally, the abstract results are applied to the time-space fractional delayed diffusion equation with fractional Laplacian operator, which improve and generalize the recent results of this issue.

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