In this paper, we propose and derive a new system called pure hybrid fuzzy neutral delay differential equations. We apply the classical fourth-order Runge–Kutta method (RK-4) to solve the proposed system of ordinary differential equations. First, we define the RK-4 method for hybrid fuzzy neutral delay differential equations and then establish the efficiency of this method by utilizing it to solve a particular type of fuzzy neutral delay differential equation. We provide a numerical example to verify the theoretical results. In addition, we compare the RK-4 and Euler solutions with the exact solutions. An error analysis is conducted to assess how much deviation from exactness is found in the two numerical methods. We arrive at the same conclusion for our hybrid fuzzy neutral delay differential system since the RK-4 method outperforms the classical Euler method.
In this Paper, We are combining so many mathematical-cum-engineering topics such as Fuzzy systems, Delay systems and Hybrid Systems under one roof called Numerical Solutions. The fuzzy valued problem was solved numerically and that approximate solution was compared with that of exact solutions. The non fuzzy and fuzzy valued numerical solutions and their graphical illustrations are also provided for the better understanding of the multiple hybrid single retarded delay problems.
This paper constructs the numerical solution of particular type of differential equations called fuzzy hybrid retarded delay-differential equations using the method of Runge-Kutta for fourth order. The concept of fuzzy number, hybrid-differential equations, and delaydifferential equations binds together to form our equations. An example following the algorithm is presented to understand the Concept of fuzzy hybrid retarded delaydifferential equations and its accuracy is discussed in terms of decimal places for easy understanding of laymen.
<abstract><p>The traditional compartmental epidemic models such as SIR, SIRS, SEIR consider mortality rate as a parameter to evaluate the population changes in susceptible, infected, recovered, and exposed. We present a modern model where population changes in mortality are also considered as the parameter. The existing models in epidemiology always construct a system of the closed medium in which they assume that new birth, as well as new death, will not be possible. But in real life, such a concept will not be assumed to not exist. From our wide observation, we find that the changing rate in every population case is notably negligible, That's why we are preferring to calculate them fractionally using FFDE. Using Lofti's fuzzy concept we are picturing the models after that we are estimating their non-integer values using three distinct methodologies LADM-4, DTM-4 for arbitrary fractional-order $ \alpha_i $, and RKM-4. At $ \alpha_{i} = 1, $ comparison of the estimations will be done. In addition to the simulation, works of numerical estimations, the existence of steady states, equilibrium points, and stability analysis are all done.</p></abstract>
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