In this article, we find the solution of time‐fractional Belousov–Zhabotinskii reaction by implementing two well‐known analytical techniques. The proposed methods are the modified form of the Adomian decomposition method and homotopy perturbation method with Yang transform. In Caputo manner, the fractional derivative is used. The solution we obtained is in the form of series which helps in investigating the analytical solution of the time‐fractional Belousov–Zhabotinskii (B‐Z) system. To verify the accuracy of the proposed methods, an illustrative example is taken, and through graphs, the solution is shown. Also, the fractional‐order and integer‐order solutions are compared with the help of graphs which are easy to understand. It has been verified that the solution obtained by using the given approaches has the desired rate of convergence to the exact solution. The proposed technique’s principal benefit is the low amount of calculations required. It can also be used to solve fractional‐order physical problems in a variety of domains.

In this article, we solve nonlinear systems of third order KdV Equations and the systems of coupled Burgers equations in one and two dimensions with the help of two different methods. The suggested techniques in addition with Laplace transform and Atangana–Baleanu fractional derivative operator are implemented to solve four systems. The obtained results by implementing the proposed methods are compared with exact solution. The convergence of the method is successfully presented and mathematically proved. The results we get are compared with exact solution through graphs and tables which confirms the effectiveness of the suggested techniques. In addition, the results obtained by employing the proposed approaches at different fractional orders are compared, confirming that as the value goes from fractional order to integer order, the result gets closer to the exact solution. Moreover, suggested techniques are interesting, easy, and highly accurate which confirm that these methods are suitable methods for solving any partial differential equations or systems of partial differential equations as well.

In this research article, we motivate and introduce the concept of possibility belief interval-valued N-soft sets. It has a great significance for enhancing the performance of decision-making procedures in many theories of uncertainty. The N-soft set theory is arising as an effective mathematical tool for dealing with precision and uncertainties more than the soft set theory. In this regard, we extend the concept of belief interval-valued soft set to possibility belief interval-valued N-soft set (by accumulating possibility and belief interval with N-soft set), and we also explain its practical calculations. To this objective, we defined related theoretical notions, for example, belief interval-valued N-soft set, possibility belief interval-valued N-soft set, their algebraic operations, and examined some of their fundamental properties. Furthermore, we developed two algorithms by using max-AND and min-OR operations of possibility belief interval-valued N-soft set for decision-making problems and also justify its applicability with numerical examples.