Generalization of Seikkala derivative and differential transform method for fuzzy Volterra integro-differential equations

Article type: Research Article

Authors: Biswas, Suvankar^{; *} | Roy, Tapan Kumar

Affiliations: Department of Mathematics, Indian Institute of Engineering Science and Technology (Formerly Bengal Engineering and Science University), Shibpur, Howrah, West Bengal, India

Correspondence: [*] Corresponding author. Suvankar Biswas, Department of Mathematics, Indian Institute of Engineering Science and Technology (Formerly Bengal Engineering and Science University), Shibpur, Howrah-711103, West Bengal, India. E-mail: suvo.rs2014@math.iiests.ac.in.

Abstract: In this study, we present a generalized concept of Seikkala differentiability for fuzzy functions. It has been shown that this concept and the lateral H-differentiability lead us to the same results. Fuzzy differential transform method (FDTM) is applied to solve fuzzy Volterra integro-differential equations. In order to show the effectiveness of this method some illustrative examples are given.

Keywords: Fuzzy derivative, generalized Seikkala derivative, fuzzy Volterra intego-differential equation, fuzzy differential transform method

DOI: 10.3233/JIFS-17958

Journal: Journal of Intelligent & Fuzzy Systems, vol. 34, no. 4, pp. 2795-2806, 2018