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 8 publications

References 47 publications

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Presentation of the efficient scheme for solving fractional order telegraph problems

Hussain,

Ali,

Fatima

et al. 2024

Partial Differential Equations in Applied Mathematics

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Presentation of the efficient scheme for solving fractional order telegraph problems

Hussain,

Ali,

Fatima

et al. 2024

Partial Differential Equations in Applied Mathematics

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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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On modified Mittag–Leffler coupled hybrid fractional system constrained by Dhage hybrid fixed point in Banach algebra

Almalahi,

Aldowah,

Alqarni

et al. 2024

Sci Rep

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This research investigates the dynamics of nonlinear coupled hybrid systems using a modified Mittag–Leffler fractional derivative. The primary objective is to establish criteria for the existence and uniqueness of solutions through the implementation of Dhage’s hybrid fixed-point theorem. The study further analyzes the stability of the proposed model. To demonstrate the practical application of this framework, we utilize a modified Mittag–Leffler operator to model the transmission of the Ebola virus, known for its complex and diverse dynamics. The analysis is conducted using a combination of theoretical and numerical methods, including transforming the system of equations into an equivalent integral form, applying the fixed-point theorem, and developing a numerical scheme based on Lagrange’s interpolation for simulating the Ebola virus model. This study aims to enhance our understanding of Ebola virus dynamics and provide valuable insights for developing effective 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 8 publications

References 47 publications

Presentation of the efficient scheme for solving fractional order telegraph problems

Presentation of the efficient scheme for solving fractional order telegraph problems

Fractal fractional model for tuberculosis: existence and numerical solutions

On modified Mittag–Leffler coupled hybrid fractional system constrained by Dhage hybrid fixed point in Banach algebra

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