Reproducing Kernel Hilbert Space Method to Solve Fuzzy Partial Volterra Integro-Differential Equations

Abstract

In this paper, a reproducing kernel Hilbert space method for the numerical solution of fuzzy partial Volterra integro-differential equations has been presented. The reproducing Hilbert space, kernel function properties, Gram-Schmidt orthogonalization process and the bounded linear operator in the same space have been developed, which helps this method to demonstrate the convergence analysis. Moreover, we present some lemmas and theorems to prove the convergence of the reproducing kernel Hilbert space method. In this method, we give the approximate solution of the fuzzy partial Volterra integro-differential equation as a Fourier series in the Hilbert space. In order to clear the efficiency of the proposed method, some numerical examples have been solved.