Abstract:
While solving practical problems, we often come across situations where the system
involves fuzziness. The mathematical models resulting in partial differential equations,
involve fuzzy parameters and variables. In available literature, methods are presented mainly
for solving non-homogeneous fuzzy partial differential equations (see Allahviranloo in Comput
Methods Appl Math 2(3):233–242, 2002; Allahviranloo and Taheri in Int JContemp Math
Sci 4(3):105–114, 2009; Allahviranloo and Afshar in Iran J Fuzzy Syst 7(3):33–50, 2010;
Allahviranloo et al. in Appl Soft Comput 11:2186–2192, 2011).We present a method to find
the solution of homogeneous fuzzy heat equations with fuzzy Dirichlet boundary conditions.
We consider the fuzziness in zero in the homogeneous equation as well as in the boundary
conditions. The initial conditions are also in fuzzy form. Further, we study the solution of
fuzzy heat equation when the fuzzy initial conditions are represent as a Fourier series.
