Numerical Solutions of Hybrid Fuzzy Differential Equations in a Hilbert Space

Abstract

The main goal of this work is to study a numerical method for certain hybrid fuzzy differential equations with an application of a reproducing kernel Hilbert space technique for fuzzy differential equations. Meanwhile, we construct a system of orthogonal functions of the space W-2(2)[a, b] circle plus W-2(2)[a, b] depending on a Gram-Schmidt orthogonalization process to get approximate-analytical solutions of a hybrid fuzzy differential equation. A proof of convergence of this method is also discussed in detail. The exact as well as the approximate solutions are displayed by a series in terms of their alpha-cut representation form in the Hilbert space W-2(2)[a, b] circle plus W-2(2)[a, b]. To demonstrate behavior, efficiency, and appropriateness of the present technique, two different numerical experiments are solved numerically in this paper. (C) 2020 IMACS. Published by Elsevier B.V. All rights reserved.