A nonlinear system of hybrid fractional differential equations with application to fixed time sliding mode control for Leukemia therapy

Ahmed, Saim; Azar, Ahmad Taher; Abdel-Aty, Mahmoud; Khan, Hasib; Alzabut, Jehad

doi:10.1016/j.asej.2023.102566

Ain Shams Engineering Journal

2024

DOI: 10.1016/j.asej.2023.102566

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A nonlinear system of hybrid fractional differential equations with application to fixed time sliding mode control for Leukemia therapy

Saim Ahmed,

Ahmad Taher Azar,

Mahmoud Abdel-Aty

et al.

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2024

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Cited by 4 publications

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Fractal fractional model for tuberculosis: existence and numerical solutions

Khan,

Shah,

Abdeljawad

et al. 2024

Sci Rep

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This paper deals with the mathematical analysis of Tuberculosis by using fractal fractional operator. Mycobacterium TB is the bacteria that causes tuberculosis. This airborne illness mostly impacts the lungs but may extend to other body organs. When the infected individual coughs, sneezes or speaks, the bacterium gets released into the air and travels from one person to another. Five classes have been formulated to study the dynamics of this disease: susceptible class, infected of DS, infected of MDR, isolated class, and recovered class. To study the suggested fractal fractional model’s wellposedness associated with existence results, and boundedness of solutions. Further, the invariant region of the considered model, positive solutions, equilibrium point, and reproduction number. One would typically employ a fractional calculus approach to obtain numerical solutions for the fractional order Tuberculosis model using the Adams-Bashforth-Moulton method. The fractional order derivatives in the model can be approximated using appropriate numerical schemes designed for fractional order differential equations.

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Fractal fractional model for tuberculosis: existence and numerical solutions

Khan,

Shah,

Abdeljawad

et al. 2024

Sci Rep

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Novel flexible fixed-time stability theorem and its application to sliding mode control nonlinear systems

Liu,

Li,

Zheng

et al. 2024

Review of Scientific Instruments

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For the fixed-time nonlinear system control problem, a new fixed-time stability (FxTS) theorem and an integral sliding mode surface are proposed to balance the control speed and energy consumption. We discuss the existing fixed time inequalities and set up less conservative inequalities to study the FxTS theorem. The new inequality differs from other existing inequalities in that the parameter settings are more flexible. Under different parameter settings, the exact upper bound on settling time in four cases is discussed. Based on the stability theorem, a new integral sliding mode surface and sliding mode controller are proposed. The new control algorithm is successfully applied to the fixed-time control of chaotic four-dimensional Lorenz systems and permanent magnet synchronous motor systems. By comparing the numerical simulation results of this paper’s method and traditional fixed-time sliding mode control (SMC), the flexibility and superiority of the theory proposed in this paper are demonstrated. Under the same parameter settings, compared to the traditional FxTS SMC, it reduces the convergence time by 18%, and the estimated upper bound of the fixed time reduction in waiting time is 41%. In addition, changing the variable parameters can improve the convergence velocity.

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Adaptive fixed-time TSM for uncertain nonlinear dynamical system under unknown disturbance

Ahmed,

Azar,

Wang

2024

PLoS ONE

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For nonlinear systems subjected to external disturbances, an adaptive terminal sliding mode control (TSM) approach with fixed-time convergence is presented in this paper. The introduction of the fixed-time TSM with the sliding surface and the new Lemma of fixed-time stability are the main topics of discussion. The suggested approach demonstrates quick convergence, smooth and non-singular control input, and stability within a fixed time. Existing fixed-time TSM schemes are often impacted by unknown dynamics such as uncertainty and disturbances. Therefore, the proposed strategy is developed by combining the fixed-time TSM with an adaptive scheme. This adaptive method deals with an uncertain dynamic system when there are external disturbances. The stability of a closed-loop structure in a fixed-time will be shown by the findings of the Lyapunov analysis. Finally, the outcomes of the simulations are shown to evaluate and demonstrate the efficacy of the suggested method. As a result, examples with different cases are provided for a better comparison of suggested and existing control strategies.

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A nonlinear system of hybrid fractional differential equations with application to fixed time sliding mode control for Leukemia therapy

Cited by 4 publications

References 47 publications

Fractal fractional model for tuberculosis: existence and numerical solutions

Fractal fractional model for tuberculosis: existence and numerical solutions

Novel flexible fixed-time stability theorem and its application to sliding mode control nonlinear systems

Adaptive fixed-time TSM for uncertain nonlinear dynamical system under unknown disturbance

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