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Looking for offer, an approximate solution of the Riccati's differential equations in this research work is based on a fuzzy linguistic model (FLM). It is shown by the FLM that it is possible to approximate continuous functions which are satisfied at the interpolation points. To obtain the function as the approximation of the solution of the RDEs, fuzzy linguistic model (FLM) was used. In numerical approaches, in order to find an approximation for a function that exists on a particular interval, just a limited number of points are utilized. However, the distinctive feature of the FLM in comparison with other approaches is that in this method all points in the arbitrary interval are used. Five examples along with their approximate solutions have been presented to show the suitability, convenience, simplicity and performance of the method. The outcomes demonstrate that the advantage of this approach compared to other methods is that there are no limiting conditions for nonlinear differential equations of order one or two with initial conditions or boundary conditions. [ABSTRACT FROM AUTHOR]

Many numerical methods have been developed for nonlinear fractional integro-differential Volterra's population model (FVPG). In these methods, to approximate a function on a particular interval, only a restricted number of points have been employed. In this research, we show that it is possible to use the fuzzy transform method (F-transform) to tackle with FVPG. It makes the F-transform preferable to other methods since it can make full use of all points on this interval. We also make a comparison showing that this method is less computational and is more convenient to be utilized for coping with nonlinear integro-differential equation (IDEs), fractional nonlinear integro-differential equation (FIDEs), and fractional ordinary differential equations (FODEs). [ABSTRACT FROM AUTHOR]