In this study, modeling the COVID-19 pandemic via a novel fractional-order SIDARTHE (FO-SIDARTHE) differential system is presented. The purpose of this research seemed to be to show the consequences and relevance of the fractional-order (FO) COVID-19 SIDARTHE differential system, as well as FO required conditions underlying four control measures, called SI,  SD,  SA, and SR. The FO-SIDARTHE system incorporates eight phases of infection: susceptible (S), infected (I), diagnosed (D), ailing (A), recognized (R), threatening (T), healed (H), and extinct (E). Our objective of all these investigations is to use fractional derivatives to increase the accuracy of the SIDARTHE system. A FO-SIDARTHE system has yet to be disclosed, nor has it yet been treated using the strength of stochastic solvers. Stochastic solvers based on the Levenberg–Marquardt backpropagation methodology (L-MB) and neural networks (NNs), specifically L-MBNNs, are being used to analyze a FO-SIDARTHE problem. Three cases having varied values under the same fractional order are being presented to resolve the FO-SIDARTHE system. The statistics employed to provide numerical solutions toward the FO-SIDARTHE system are classified as obeys: 72% toward training, 18% in testing, and 10% for authorization. To establish the accuracy of such L-MBNNs utilizing Adams–Bashforth–Moulton, the numerical findings were compared with the reference solutions.

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This study presents the applications of the extended rational sine-cosine/sinh-cosh schemes to the Klein-Gordon-Zakharov equations and the (2+1)-dimensional Maccari system. Various wave solutions such as singular periodic, periodic wave, topological, topological kink-type, dark and singular soliton solutions are successfully revealed. To display the physical features of the reported solutions, we use some appropriate choice of parameters in plotting the 3D, 2D, and contour graphs of some attained solutions.

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