Future Challenges in the Fractional-Order Dynamical Systems: From Mathematics to Applications

The existence of fractional evolution equations has attracted a growing interest in recent years. The mild solution of fractional evolution equations constructed by a probability density function was first introduced by El-Borai. Inspired by El-Borai, Zhou and Jiao gave a definition of mild solution for fractional evolution equations with Caputo fractional derivative. Exact controllability is one of the fundamental issues in control theory: under some admissible control input, a system can be steered from an arbitrary given initial state to an arbitrary desired final state. In this article, using the (α, β) resolvent operator and three different fixed point theorems, we discuss the control problem for a class of Hilfer fractional Langevin evolution equations. The exact controllability of Hilfer fractional Langevin systems is established. An example is also discussed to illustrate the results.

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2 citations

Original Research

08 June 2023

Malware propagation model of fractional order, optimal control strategy and simulations

Ying Zhou

, 2 more and

Shou-Feng Shen

1,737 views

3 citations

Original Research

05 May 2023

Dynamical behaviors of an epidemic model for malware propagation in wireless sensor networks

Ying Zhou

, 3 more and

Wen-Xiu Ma

To explore malware propagation mechanisms in networks and to develop optimal strategies for controlling the spread of malware, we propose a susceptible-unexposed-infected-isolation-removed epidemic model. First, we establish a non-linear dynamic equation of malware propagation. Then, the basic reproductive number is derived by using the next-generation method. Finally, we carry out numerical simulations to observe the malware spreading in WSNs to verify the obtained theoretical results. Furthermore, we investigate the communication range of the nodes to make the results more complete. The optimal range of the nodes is designed to control malware propagation.

2,726 views

9 citations