The purpose of this work is to provide a stochastic framework based on the scale conjugate gradient neural networks (SCJGNNs) for solving the malaria disease model of pesticides and medication (MDMPM). The host and vector populations are divided in the mathematical form of the malaria through the pesticides and medication. The stochastic SCJGNNs procedure has been presented through the supervised neural networks based on the statics of validation (12%), testing (10%), and training (78%) for solving the MDMPM. The optimization is performed through the SCJGNN along with the log-sigmoid transfer function in the hidden layers along with fifteen numbers of neurons to solve the MDMPM. The accurateness and precision of the proposed SCJGNNs is observed through the comparison of obtained and source (Runge-Kutta) results, while the small calculated absolute error indicate the exactitude of designed framework based on the SCJGNNs. The reliability and consistency of the SCJGNNs is observed by using the process of correlation, histogram curves, regression, and function fitness.

The present manuscript gives an overview of how two-dimensional heat diffusion models underwent a fractional transformation, system coupling as well as solution treatment. The governing diffusion models, which are endowed with Caputo's fractional-order derivatives in time $t$, are suitably coupled using the (1) convection phenomenon, (2) interfacial coupling by considering the mechanism of a double-layered bar, and the (3) nonlinear coupling due to temperature-dependent thermal diffusivities. Semi-analytical and analytical methods are considered for the solution treatment. Moreover, we seek a computational environment to graphically illustrate the systems' response to different fractional orders in each case through the determined diffusional fields. Besides, we supply certain concluding notes at the end.