New implementation of reproducing kernel Hilbert space method for solving a fuzzy integro-differential equation of integer and fractional orders

Abstract

This paper presents a novel technique for solving two new form of equation with fuzzy and integro-differential equations. The proposed numerical iterative technique is based on the use of the reproducing Kernel theory. Two numerical examples are given to show the effectiveness and performance of the proposed technique. Simulation results are illustrated and comparative studies with past published works to the exact solution from Laplace transform of order integer have been performed to emphasize the simplicity and accuracy of the proposed technique. Moreover, future applications of the proposed technique are also discussed. Numerical experimental results fully support the findings of the proposed analytical approaches. Keywords: Fuzzy integro-differential, Fractional calculus, Caputo and Riemann-Liouville definitions, Reproducing Kernel theory