Abstract
In this paper, we provide the generalization of two predefined concepts under the name fuzzy conformable differential equations. We solve the fuzzy conformable ordinary differential equations under the strongly generalized conformable derivative. For the order $\Psi$, we use two methods. The first technique is to resolve a fuzzy conformable differential equation into two systems of differential equations according to the two types of derivatives. The second method solves fuzzy conformable differential equations of order $\Psi$ by a variation of the constant formula. Moreover, we generalize our results to solve fuzzy conformable ordinary differential equations of a higher order. Further, we provide some examples in each section for the sake of demonstration of our results.
Highlights
Any or most of the data may sometimes be ambiguous when modeling real-world phenomena
We provide the generalization of two predefined concepts under the name fuzzy conformable differential equations
The first technique is to resolve a fuzzy conformable differential equation into two systems of differential equations according to the two types of derivatives
Summary
Any or most of the data may sometimes be ambiguous when modeling real-world phenomena. To study the solution of fuzzy initial and boundary value problems, we need the concept of derivative of fuzzy-valued functions [2]. Bede [6] introduced a generalization of H-derivative based on the lateral type of derivatives called strongly generalized differentiability This concept allows us to cope with the above-mentioned shortcomings. The solution of differential equations is difficult to obtain using these definitions, see for example [12] To overcome these disadvantages, Khalil [13] introduced a new definition of fractional derivative called conformable derivative. Fuzzy conformable derivative of order Ψ was introduced by ([24], [25]) and used in [26] to solve fuzzy conformable differential equations. We obtain solutions of higher-order fuzzy fractional differential equations of conformable type.
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