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Typically, the parameters of a practical problem are considered to be deterministic. Nevertheless, there may be possibility that these parameters are incomplete owing to observational or experimental errors. Fuzzy sets are capable of handling such problems. In addition, the majority of studies on fuzzy fractional heat equations have employed two spatial variables and fuzzy sets with deterministic membership. In some instances, however, there may be more than two spatial variables, and the membership grade associated with an uncertain parameter may also contain imprecise information. Consequently, dealing with such a situation may be fascinating. In this regard, the main objective of this research is to develop alternative methods for solving the n+1-dimensional fractional order heat equation with an external source term in an uncertain environment. The problem is addressed by using the Elzaki transformed homotopy perturbation method and the fractional reduced differential transformation method in the fuzzy environment. Caputo fuzzy fractional derivatives are considered here. In this study, triangular fuzzy numbers and Gaussian fuzzy numbers are utilised to handle type-1 fuzzy uncertainty, whereas triangularly perfect quasi type-2 fuzzy numbers and newly introduced Gaussian-triangular type-2 fuzzy numbers are used to handle type-2 fuzzy uncertainty. Numerical examples with graphical representations are provided to demonstrate the applicability of the approaches. Convergence plots are also provided.

In recent years, the study of mathematical models for the human immunodeficiency virus (HIV) has attracted considerable interest due to its importance in comprehending and combating the propagation of the virus. Typically, the model's governing equations are a system of ordinary differential equations. In order to explain the inheritance behavior, fractional order HIV models may be more helpful than integer order models. In addition, the presence of uncertainty in real-world phenomena can not be avoided, and fuzzy numbers are of great use in these scenarios. In view of the above, the numerical solution of the fuzzy fractional order HIV model is analyzed in this paper. The model takes into account the interactions between susceptible, asymptomatic, and symptomatic populations, as well as the effects of fractional order derivatives and fuzzy uncertainty. Here, the differentiation of the fuzzy parameters is considered in granular sense. The uncertain model parameters are addressed with triangular fuzzy numbers (TFNs) and interval type-2 triangular fuzzy numbers (IT2TFNs). The use of interval type-2 fuzzy numbers rather than type-1 fuzzy numbers to express the imprecise parameters may be helpful in some instances where the membership grade is unclear. The generalized modified Euler method (GMEM) is used to derive the corresponding solutions. Lastly, the behavior of various populations in crisp as well as uncertain environments is also studied using graphical results.