Solving fuzzy fractional q-differential equations via fuzzy q-differential transform

Article type: Research Article

Authors: Osman, Mawia | Xia, Yonghui^{; *}

Affiliations: College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua, China

Correspondence: [*] Corresponding author. Yonghui Xia. E-mail: yhxia@zjnu.cn.

Abstract: This paper proposes a method for solving fuzzy linear and nonlinear partial q-differential equations by the fuzzy q-differential transform. Further, we implemented the fuzzy fractional q-differential transform for solving some types of fuzzy fractional q-differential equations. The technique investigated is based on gH-differentiability, fuzzy q-derivative, and fuzzy q-fractional derivative. Various concrete problems have been tested by implementing the new method, and the results show great performance. The results also reveal that the method is a very effective and quite accurate mathematical tool for solving fuzzy fractional and integer q-differential equations. Finally, we have provided some examples illustrating our method.

Keywords: Fuzzy numbers, fuzzy-valued functions, fuzzy q-derivative; fuzzy q-fractional derivative, gH-differentiability, fuzzy q-differential transform method

DOI: 10.3233/JIFS-222567

Journal: Journal of Intelligent & Fuzzy Systems, vol. 44, no. 2, pp. 2791-2846, 2023