The existence and uniqueness of fuzzy solutions for hyperbolic partial differential equations
Fuzzy hyperbolic partial differential equation, one kind of uncertain differential equations, is a very important field of study not only in theory but also in application. This paper provides a theoretical foundation of numerical solution methods for fuzzy hyperbolic equations by considering sufficient conditions to ensure the existence and uniqueness of fuzzy solution. New weighted metrics are introduced to investigate the solvability for boundary valued problems of fuzzy hyperbolic equations and an extended result for more general classes of hyperbolic equations is initiated. Moreover, the continuity of the Zadehs extension principle is used in some illustrative examples with some numerical simulations for \(\alpha \)-cuts of fuzzy solutions.
fuzzy solution fuzzy partial differential equation integral boundary condition local initial condition fixed point theorem 34a07 34a99 35l15