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Mathematics, Applied
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Summary: Research on immunogenic tumor dynamics based on a fractional model involves investigating stability, equilibrium points, and implementing a modified predictor-corrector method. Results show the new model provides flexibility in adjusting complex dynamics and implementing a tracking control method can decrease tumor-cell population development. The satisfaction of control purpose is confirmed by simulation results tracking tumor-free steady state in realistic cases.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
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(2022)
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Summary: This paper investigates a fractional order nonlinear mathematical model describing the dynamics of atmospheric CO2 concentration, examining the impact of forest biomass and human population variations on CO2 dynamics. The study utilizes Caputo fractional derivatives and demonstrates the computational strength of the employed scheme. It also analyzes the uniqueness and convergence of obtained solutions for a fractional model.
CHAOS SOLITONS & FRACTALS
(2021)
Article
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Summary: This paper investigates the hyperchaos analysis, optimal control, and synchronization of a nonautonomous cardiac conduction system. Various approaches are used to analyze, control, and synchronize the hyperchaotic behaviors, demonstrating the efficacy of proposed strategies through simulation and theoretical justification. The new nonlinear fractional model shows more flexible behavior than its classical counterpart due to its memory effects.
ADVANCES IN DIFFERENCE EQUATIONS
(2021)
Article
Mathematics, Interdisciplinary Applications
Sania Qureshi et al.
Summary: A new epidemiological model considering both integer and fractional order operators was developed to study the transmission dynamics of measles. Stability analysis and parameter sensitivity were discussed, with optimization of the fractional order parameter chi. Various simulations were conducted to observe the effects of parameters on the dynamics of the epidemic.
CHAOS SOLITONS & FRACTALS
(2021)
Article
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A. Jajarmi et al.
Summary: In this study, a new fractional formulation is presented to investigate the complex behaviors of a capacitor microphone dynamical system. By constructing Euler-Lagrange equations and using matrix approximation technique, a nonlinear algebraic system is derived and solved numerically, revealing various features different from previous mathematical formalism.
RESULTS IN PHYSICS
(2021)
Article
Mathematics, Applied
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Summary: This paper analyzes the dynamic motion of a quarter-car suspension system with sinusoidal road excitation force, introducing a new fractional-order differential equations mathematical model and proposing a quadratic numerical method to solve the related equations. By investigating time-domain responses and phase portraits, both chaotic and non-chaotic behaviors of the system can be identified through the fractional-order model. A state-feedback controller and chaos optimal control are presented to overcome chaotic oscillations in the system, with simulation results demonstrating the effectiveness of the proposed modeling and control strategies.
ADVANCES IN DIFFERENCE EQUATIONS
(2021)
Article
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Summary: This paper discusses a new COVID-19 SIR model with three classes (Susceptible, Infected, and Recovered) and Convex incidence rate, presenting differential equations, disease-free and endemic equilibrium, basic reproduction number R-0, and Global Stability analysis. The model is validated through numerical simulation using data from Pakistan, showing how protection, exposure, and death rates of the different populations evolve over time.
RESULTS IN PHYSICS
(2021)
Article
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Sania Qureshi et al.
Summary: The study investigates the logistic growth model in population dynamics using both classical and non-classical differential operators with actual statistical data. The results suggest the superiority of the fractional conformable logistic model, which is explored for uniqueness through fixed point theory. Numerical simulations using the Adams iterative technique illustrate the model's behavior and provide a statistical summary of the operators.
Article
Mathematics, Applied
Dumitru Baleanu et al.
Summary: This paper introduces and analyzes a novel fractional chaotic system with quadratic and cubic nonlinearities. Numerical simulations determine the lowest order at which the system remains chaotic, and the system's chaotic behavior is studied using a nonstandard finite difference scheme. Additionally, nonidentical synchronization between the model and fractional Volta equations is achieved through an active control strategy, confirming its effectiveness through simulations.
ADVANCES IN DIFFERENCE EQUATIONS
(2021)
Article
Mathematics
Sania Qureshi
Summary: This study investigates the second order linear ordinary differential equation mass spring damper system using the Sumudu integral transform and Caputo type differential operator to find a closed form solution. The solution, in terms of the Fox H-function, offers different aspects depending on the values of alpha (in (1,2]) and beta (in (0,1]). The classical mass spring damper model is obtained when alpha = beta = 1.
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(2021)
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(2020)
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(2020)
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RESULTS IN PHYSICS
(2020)
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Mathematics, Interdisciplinary Applications
Jagdev Singh
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(2020)
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COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2010)
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Zhanbing Bai
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(2010)
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(2009)
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Qasem M. Al-Mdallal
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(2009)
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S. C. Brailsford et al.
JOURNAL OF SIMULATION
(2009)
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SI Muslih et al.
