LAUSR

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 ] ⊕ 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 α-cut representation form in the Hilbert space W 2 2 [ a , b ] ⊕ 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.