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![Triangular fuzzy number and its r-level is: [] = [ ( − ), − ( − )], ∈ [0, 1]](profile/Ali-Jameel-2/publication/281834573/figure/fig1/AS:613967961542656@1523392777086/Triangular-fuzzy-number-and-its-r-level-is---0-1.png)
Triangular fuzzy number and its r-level is: [] = [ ( − ), − ( − )], ∈ [0, 1]
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![Fig. 1. Triangular fuzzy number and its r-level is: [] = [ ( − ), − ( −...](profile/Ali-Jameel-2/publication/281834573/figure/fig1/AS:613967961542656@1523392777086/Triangular-fuzzy-number-and-its-r-level-is---0-1_Q320.jpg)
In this paper, we develop and analyze the use of the Homotopy Perturbation Method (HPM) to find the
approximate analytical solution for an initial value problem involving the fuzzy parabolic equation. HPM
allows for the solution of the partial differential equation to be calculated in the form of an infinite series in
which the components can be ea...
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Citations
... These models are used in various applications including population models (Omer & Omer, 2013; Tapaswini, & Chakraverty, 2013), quantum optics gravity (El Naschie, 2005), medicine (Abbod et al., 2001) etc. In recent years semi analytical methods such as Homotopy Perturbation Method (HPM) have been used to solve fuzzy problems involving ordinary differential equations (Jameel & Ahmad Izani, 2015; Jameel & Ahmad Izani, 2014; Jameel, & Hamzeh, 2015). The major disadvantage in the traditional perturbation technique is the over dependence on the existence of small parameter. ...
In this study, the Homotopy Perturbation Method (HPM) is modified and formulated to find the Semi analytical solution for an initial value problem involving the system of linear fuzzy differential equation. HPM allows for the solution of the differential equation to be calculated in the form of an infinite series in which the components can be easily computed. The HPM is studied for fuzzy initial value problems involving ordinary differential equations. Also HPM is constructed and formulated to obtain a semi analytical solution of system of linear fuzzy differential equation using the properties of fuzzy set theory. The effectiveness of the algorithm is demonstrated for solving system of linear fuzzy differential equation is solved to illustrate the capability of HPM.
