Numerical investigation of fluid dynamic model in uncertain environment. (English) Zbl 1543.34050
Summary: Cerebrospinal fluid (CSF) circulation abnormalities are a severe ailment known as hydrocephalus. Further, the presence of uncertainty can not be neglected in such practical scenarios. Fuzzy numbers can play a great role in these circumstances. The use of type-2 fuzzy numbers can be beneficial as they explain the model more accurately because there may be some vagueness in the membership too. This research is devoted to the numerical study of the CSF pressure model of fractional order in type-2 fuzzy uncertain environment. The homotopy perturbation method (HPM) and the Adomian decomposition method (ADM), are used to solve the problem. In this study, the involved initial condition is assumed to be type-2 fuzzy in behaviour. Few numerical examples are provided to demonstrate the applicability of both schemes. The behaviour of the model for various numerical values of the parameters is studied using tables and two- and three-dimensional plots.
MSC:
34C60 | Qualitative investigation and simulation of ordinary differential equation models |
92C35 | Physiological flow |
34A07 | Fuzzy ordinary differential equations |
34A08 | Fractional ordinary differential equations |
34A45 | Theoretical approximation of solutions to ordinary differential equations |
26E50 | Fuzzy real analysis |