Abstract
In this paper, we use an intuitionistic fuzzy Laplace transforms for solving intuitionistic fuzzy hyperbolic equations precisely the transport equation with intuitionistic fuzzy data under strongly generalized H-differentiability concept. For this purpose, the intuitionistic fuzzy transport equation is converted to the intuitionistic fuzzy boundary value problem (IFBVP) based on the intuitionistic fuzzy laplace transform. The related theorems and properties are proved in detail. Finally, we solve an example to illustrate this method.
Highlights
A simple approach to model propagation phenomena that emerge naturally under uncertainty is to use intuitionistic fuzzy partial differential equations (IFPDE)
An archetype of the intuitionistic fuzzy hyperbolic equations is the transport equation, wich can appear in many applications such as fluid mechanics, the dynamics of particuler interacting with matter
The notion of intuitionistic fuzzy set was first presented by Atanassov [1, 2] as a generalization of the notion of fuzzy set, that is introduced by Zadeh (1965) [13], the authors in [3, 4] are discussed Fuzzy laplace transform and Solving fuzzy Duffing’s equation by the laplace transform decomposition, the idea of intuitionistic fuzzy metric space and Fuzzy differential systems under generalized metric spaces approach are presented in [7, 9], while in [] the theorem of the existence of the soultion for intuitionistic fuzzy transport equations are proved
Summary
A simple approach to model propagation phenomena that emerge naturally under uncertainty is to use intuitionistic fuzzy partial differential equations (IFPDE). This work is motivated by the solution of a intuitionistic fuzzy transport equation using the intuitionistic fuzzy Laplace transform. This appears to be one of the first attempts to solve one of the first attempts to solve these well known intuitionistic fuzzy partial differential equations under a strongly generalized Hdifferentiability.
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