Abstract
A class of linear impulsive fuzzy dynamic equations on time scales is considered by using the generalized differentiability concept on time scales. Some novel criteria and general forms of solutions are established for such models whose significance lies in proposing the possibility to get unifying forms of solutions for discrete and continuous dynamical systems under uncertainty and to unify corresponding problems in the framework of fuzzy dynamic equations on time scales. Finally, some examples show the applicability of our results.
Highlights
In the real world, some processes vary continuously, while others vary discretely. ese processes can be modeled by differential and difference equations, respectively. ere are some processes that vary both continuously and discretely
Much progress has been seen in the fuzzy differential equation direction, and many criteria are established based on different approaches
Careful investigation reveals that it is similar to explore the existence of solutions for fuzzy differential equations and their discrete analogue in the approaches, methods, and the main results
Summary
Some processes vary continuously, while others vary discretely. ese processes can be modeled by differential and difference equations, respectively. ere are some processes that vary both continuously and discretely. E first approach to modeling the uncertainty of dynamical systems uses the H-derivative or its generalized, and mainly the existence and uniqueness of the solution of a fuzzy differential equation are studied under this setting (see for example [11, 14, 33,34,35]). It contains the ΔH-derivative introduced in [41].
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