|
|
 |
| |
|
|
|
A Fractional Fuzzy Dynamical Model for Math-Phobia with Optimal Learning Intervention Strategies |
|
|
|
PP: 531-548 |
|
|
doi:10.18576/pfda/120304
|
|
|
|
Author(s) |
|
|
|
M. Ariyanatchi,
P. Roselyn Besi,
I. Paulraj Jayasimman,
Ali Akgu ̈l,
M. Qasymeh,
M. Abdel-Aty,
M. Hafez,
|
|
|
|
Abstract |
|
|
| This paper introduces a new six-compartment fuzzy fractional-order epidemic model that describes the spread and mitigation of math-phobia in student populations. The susceptible S ̧ (t), mathphobic M(t), not interested N(t), intervention-aware A(t), interested l(t), and recovered R(t) compartments capture key behavioural transitions influenced by psychological, social, and educational factors. Caputo-type fuzzy fractional differential equations are used to derive these dynamics, considering memory effects and epistemic uncertainty in the transmission and recovery rates. By applying fixed-point theory, we prove the existence and uniqueness of the solution under fuzzy initial conditions, hence guaranteeing mathematical coherence of the model. The idea is that an optimal control framework is incorporated in the design of time-dependent strategies such as workshops for anxiety reduction, pedagogy that is engaging, motivational counselling, and cognitive restructuring that aim at reducing math-phobia and apathy while improving interest and resilience. The system is solved via a fuzzy Laplace–Adomian decomposition scheme, and numerical simulations illustrate that combined interventions have a significant decrease in the math-phobic and apathetic populations with an increase in the proportion of interested and recovered individuals. The results provide a quantitative backbone for evidence-based educational policies in dealing with math anxiety in learning environments. |
|
|
|
|
|
|
|
