On solution of fuzzy Volterra integro-differential equations

Abstract

In this article, the Volterra integro-differential equation of separable type kernels is considered under the fuzzy concept. A hybrid technique is used to solve fuzzy integro-differential equations under the notion of generalized Hukuhara differentiability. To build up a suitable algorithm, Laplace transformation coupled with the Adomian decomposition method (LADM) is used which is an essential and profitable algorithm for setting the fuzzy Volterra integro-differential equations. The proposed method is illustrated by two test problems that show the convergence of the series solution to the exact solution in closed form. The numerical results of the examples are depicted by appropriate graphs at different uncertainty values. Additionally, the graphical portrayals show the fruitfulness and accuracy of the proposed method.

Keywords

• fuzzy integro-differential equation
• semi-analytical solution
• laplace transformation
• adomian decomposition method
• hukuhara differentiability