Abstract
The main focus of this paper is to develop an efficient analytical method to obtain the traveling wave fuzzy solution for the fuzzy generalized Hukuhara conformable fractional equations by considering the type of generalized Hukuhara conformable fractional differentiability of the solution. To achieve this, the fuzzy conformable fractional derivative based on the generalized Hukuhara differentiability is defined, and several properties are brought on the topic, such as switching points and the fuzzy chain rule. After that, a new analytical method is applied to find the exact solutions for two famous mathematical equations: the fuzzy fractional wave equation and the fuzzy fractional diffusion equation. The present work is the first report in which the fuzzy traveling wave method is used to design an analytical method to solve these fuzzy problems. The final examples are asserted that our new method is applicable and efficient.
Highlights
IntroductionThe interest of mathematicians in fuzzy differential equations has been rapidly increasing
During the last decade, the interest of mathematicians in fuzzy differential equations has been rapidly increasing
The fuzzy fractional wave equation and fuzzy Diffusion equation are introduced based on the generalized Hukuhara conformable fractional differentiability
Summary
The interest of mathematicians in fuzzy differential equations has been rapidly increasing. Hoa et al [20] introduced the fuzzy Caputo-Katugampola fractional differential equations in fuzzy space, and under generalized Lipschitz condition, the existence and uniqueness of the solution proved. It is well-known that the usual Hukuhara difference between two fuzzy numbers exists only under very restrictive conditions [16, 9] To overcome this shortcoming, we will introduce the fuzzy conformable fractional derivative under generalized Hukuhara differentiability, and prove some important properties for this kind of differentiability. The main contribution of this paper is to find the wave traveling solutions for the problem (1) For this purpose, the concept of generalized Hukuhara conformable fractional differentiability is introduced thoroughly in the fuzzy functions. The fuzzy fractional wave equation and fuzzy Diffusion equation are introduced based on the generalized Hukuhara conformable fractional differentiability.
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