Abstract
In this paper, we introduce a new metric space to study the existence and uniqueness of solutions to second order fuzzy dynamic equations on time scales. In this regard, we use Banach’s fixed point theorem to prove this result. Also, we see that this metric guarantees an elegant and easier proof for the existence of solutions to second order fuzzy dynamic equations on time scales.
Highlights
One of the most interesting and significant discussions in the field of differential equations is dynamic equations on time scales
The main aim of this paper is to prove the existence and uniqueness of solutions to second order fuzzy dynamic equations on time scales, and we put off discussing this problem to Section
We introduce a new metric on the set of the fuzzy continuous functions on time scales and use it to define another new metric space
Summary
One of the most interesting and significant discussions in the field of differential equations is dynamic equations on time scales. As the second step, it is natural to investigate the existence and uniqueness of solutions to fuzzy dynamic equations on time scales. The main aim of this paper is to prove the existence and uniqueness of solutions to second order fuzzy dynamic equations on time scales, and we put off discussing this problem to Section. We introduce a new metric on the set of the fuzzy continuous functions on time scales and use it to define another new metric space. [ , ] Let u, v ∈ RF be two fuzzy numbers; (i) if the gH-difference exists, it is unique; (ii) u gH v = u v or u gH v = –(u v) whenever the expressions on the right exist; in particular, u gH u = u u = ̃ ;.
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