**Atanaska Georgieva**

Department of Mathematical Analysis, University of Plovdiv Paisii Hilendarski, 24 Tzar Asen, 4003 Plovdiv, Bulgaria; afi2000@abv.bg

Received: 24 March 2020; Accepted: 24 April 2020; Published: 2 May 2020

**Abstract:** In this paper, the double fuzzy Sumudu transform (DFST) method was used to find the solution to partial Volterra fuzzy integro-differential equations (PVFIDE) with convolution kernel under Hukuhara differentiability. Fundamental results of the double fuzzy Sumudu transform for double fuzzy convolution and fuzzy partial derivatives of the *n*-th order are provided. By using these results the solution of PVFIDE is constructed. It is shown that DFST method is a simple and reliable approach for solving such equations analytically. Finally, the method is demonstrated with examples to show the capability of the proposed method.

**Keywords:** double fuzzy Sumudu transform; partial Volterra fuzzy integro-differential equations; *n*-th order fuzzy partial *H*-derivative
