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This study aims to address the difficulties in solving coupled generalized non-linear Burger equations using local fractional calculus as a framework. The methodology used in this work, particularly in the area of local fractional calculus, combines the Elzaki transform with the Adomian decomposition method. This combination has proven to be a highly effective strategy for addressing non-linear partial differential equations within the local fractional context, which finds numerous practical applications. The proposed method offers a systematic and easily understandable procedure for tackling both linear and non-linear partial differential equations (PDEs). It provides an easy-to-follow path to solve these problems. We offer a real-world example that exhibits the method's successful use in resolving issues to corroborate its efficacy. The obtained solution is visually represented to illustrate the practical utility of this approach. [ABSTRACT FROM AUTHOR]

The current study provides the solutions of the mathematical model based on the coronavirus including the effects of vaccination and quarantine. The numerical stochastic process relying on Levenberg-Marquardt backpropagation technique (L-MB) neural networks (NN), i.e., L-MBNNs, is presented to solve the model. The entire dynamics of the proposed model depends upon the human population, which is represented by N and is further divided into multiple subgroups. The detail of these subgroups is presented in the form of susceptible population (S), exposed population (E), and infected people (I). Likewise, Q represents the quarantined and R shows the recovered or deceased individuals. Those who have been immunized are symbolized by V. All these categories make the model SEIQRV, that is based on a system of nonlinear differential equations. The statistics that is used to provide the numerical solutions of the SEIQRV model is 76% for training, 10% for testing and 14% for authorization. The correctness of the L-MBNNs is tested by using the comparison of the proposed and reference solutions (Adam method). The statistical representations are provided in order to check the reliability, competence and validity of L-MBNNs using the procedures of error histograms (EH), state transitions (ST), regression and correlation. [ABSTRACT FROM AUTHOR]