Abstract
In this chapter, the mathematical model spread of infectious diseases exemplifying the effects of awareness programs by media is studied with the help of newly proposed fractional operators. The solution for the system of equations exemplifying the model is obtained with the help of the q-homotopy analysis transform technique (q-HATT). The projected method is an elegant amalgamation of the q-homotopy analysis scheme and the Laplace transform. Three fractional operators are employed in this study to show their essence in generalizing the models associated with power-law distribution: kernel singular, nonlocal, and nonsingular. The fixed-point theorem employed to present the existence and uniqueness for the hired arbitrary-order model and converges for the solution is derived with Banach space. The projected scheme springs the series solution rapidly convergent, and it can guarantee the convergence associated with the homotopy parameter. Moreover, for diverse fractional-order, the physical nature has been captured in plots.
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