Numerical Solution Of Nonlinear Fractal–Fractional Dynamical Model Of Interpersonal Relationships With Power, Exponential And Mittag-Leffler Laws

The term fractional differentiation has recently been merged with the term fractal differentiation to create a new fractional differentiation operator. Several kernels were used to explore these new operators, including the power-law, exponential decay, and Mittag-Leffler functions. In this study, we analyze three forms of interpersonal relationships model. The numerical solution of the fractal–fractional interpersonal relationships model based on different kernels has been investigated. The new operators contain two parameters: one is for fractional order α, and the other is for fractal dimension γ. We use Lagrangian polynomial interpolation along with numerical method and the concept of fractional theory to solve these three forms of the titled model. All three forms of the numerical computation are compared with the solutions of the other existing method when α = γ = 1 that leads to a good agreement. The existence and uniqueness of the models have been studied using the Picard–Lindelöf theorem. To understand how the effects of fractal dimension and fractional order influence the model, we have illustrated various plots taking different values of α and γ.